Adaptive Optimization of Decision Making for Vehicle Control

ABSTRACT

A control system for controlling a motion of a vehicle to a target driving goal uses a decision-maker configured to determine a sequence of intermediate goals leading to the next target goal by optimizing the motion of the vehicle subject to a first model and tightened driving constraints formed by tightening driving constraints by a safety margin, and uses a motion planner configured to determine a motion trajectory of the vehicle tracking the sequence of intermediate goals by optimizing the motion of the vehicle subject to the second model. The driving constraints include mixed logical inequalities of temporal logic formulae specified by traffic rules to define an area where the temporal logic formulae are satisfied, while the tightened driving constraints shrink the area by the safety margin, which is a function of a difference between the second model and the first model approximating the second model.

TECHNICAL FIELD

The present disclosure relates generally to autonomous driving andadvanced driver-assistance systems, and, more particularly, to determinea sequence of decisions for controlling a motion of the vehicleoptimized for different traffic situations.

BACKGROUND

Conventional autonomously driving vehicles are equipped with a controlsystem that determines how the vehicle should move on the road,accounting legal driving rules and traffic, to achieve its drivingobjectives. The conventional control system determines the vehiclemotion by analyzing the environment based on data acquired by thesensors and processed by recognition and mapping algorithms, bycomputing a desired vehicle path and speed, and by controlling thevehicle to follow that path using available vehicle actuators. Due tothe complexity of such conventional operations, some conventionalcontrol systems include separated components responsible for pathplanning and vehicle control. For instance, U.S. Pat. No. 9,915,948discusses how the vehicle control and the path planning can beintegrated to guarantee that the vehicle achieves a desired objective ofthe driving.

For example, the path planning of the autonomous vehicle can execute amotion planning system (MPS) responsible for determining path and/ormotion trajectory of the vehicle. MPS can use different path planningmethods, see for instance U.S. Pat. No. 9,568,915. To determine a motiontrajectory to reach a target goal, the MPS can use knowledge of thecurrent and predicted environment, obtained from vehicle sensors orreceived over communication channels as well as maps of the environment.To be able to adjust the motion trajectory according to the changingenvironment, the MPS needs to continuously update the motion trajectoryin real-time, with limited computations due to the limited capabilitiesof computing and communication platforms in the vehicle.

Accordingly, due to the need to operate in real-time to account fordynamic and rapidly changing environment, the motion trajectory can bepredicted only for a brief period of time, i.e., a planning interval ofthe MPS is not able to cover the entire driving path of the vehicle butonly a certain sub-segment, from the current position to a nextintermediate driving goal. In complex dynamic scenarios, such asautonomous driving in urban settings, there may be multiple sequences ofintermediate goals that may all lead to a successful completion of thetrip. On the other hand, some of the intermediate goals that arepossibly achievable by the vehicle may fail to achieve the targetdriving goal, due to potential violation of the traffic rules and/orcollisions with other vehicles. Hence, some intermediate goals mayactually be impossible to achieve for the vehicle motion, and ifprovided to the MPS, the autonomous control of the vehicle would fail.

To that end, there is a need for a decision making mechanism to make adecision about a sequence of intermediate goals that motion trajectoryneeds to achieve in order to achieve the overall goal of driving.

SUMMARY

It is an object of some embodiments to provide a decision making system(DMS) configured to select intermediate goals to be tracked by a motiontrajectory of a vehicle on its path to a target goal. Additionally oralternatively, it is an object of some embodiments to provide such a DMSthat selects each intermediate goal optimally so that: (i) the goal isachievable by the vehicle, (ii) achieving the goal satisfies the trafficrules, (iii) achieving the goal does not causes negative interactions,e.g., collisions, with other vehicles, and (iv) achieving a finitesequence of intermediate goals results necessarily in achieving thetarget driving goal, i.e., the completion of the trip or a desiredsection of the trip. Additionally, or alternatively, it is an object ofsome embodiments to provide such a DMS for which the computation of theintermediate goals is (v) suitable to be executed in real-time by theautonomous vehicle computational unit, in order to account for the needto frequently re-compute intermediate goals according to dynamicallychanging environment, and (vi) safe, i.e., the simplification of thecomputation should not jeopardize the safety of actual control of thevehicle. However, a DMS that achieves objectives (i)-(vi) is challengingto design.

Some embodiments are based on realization that a DMS that achievesobjectives (i)-(iv) can be constructed using a formal specification ofthe traffic rules and interactions of the vehicle and obstacles usingsignal temporal logic, which are combined with motion models forvehicles and obstacles. It also realized that by converting theresulting formal specifications into an optimization problem, theoptimal solution of such problem provides the sequence of goals for theMPS, that are guaranteed to satisfy the objectives (i)-(iv). However,the obtained optimization problem is a nonlinear mixed integer program(NLMIP), which does not satisfy objective (v) because the solution ofNLMIP in general may not be computed. In some situations, evenattempting the NLMIP computation is not possible in real-time inautomotive-grade computing platforms. To overcome that, in someembodiments, the motion model of the vehicle moving on a road havingobstacles is approximated. In this way the optimization problem itselfcan be approximated as a mixed integer program (MIP) for whichcomputation of the solution can be guaranteed, also in real-time, thusachieving the objective (v).

On the other hand, the approximation of the vehicle and traffic motionmay lead to generating a sequence of intermediate goals that appear tobe satisfying (i)-(iv) according to the approximated motion models,while the (i)-(iv) are not achievable according to the correct motionmodel, i.e., the motion model used by a motion planning system (MPS)thereby causing the MPS to fail. This is due to the solution notsatisfying (vi), i.e., not being robust to modeling error. Robustifyingthe approximated motion model is known to be computationally expensive.

Thus, in order to achieve the objective (vi) which allows to maintainobjectives (i)-(iv) in presence of approximated models needed to achievethe objective (v), some embodiments, instead of robustifying theapproximated motion model, robustify the formal specifications byrequesting not only that the specifications are satisfied, but that theyare satisfied with a pre-described safety margin, related to the (e.g.,worst case) difference between the motion model used in MPS and theapproximated motion model used in DMS. In this way, satisfaction of thespecifications by DMS according to the approximated motion model withinthe pre-described safety margin, leads to the MPS being able to satisfythe actual specifications, without such margin, according to the vehiclemotion model.

Additionally, or alternatively, some embodiments are based on anotherrealization that adding tightened specifications to ensure thesatisfaction of objectives (v)-(vi) may destroy well-defined structureof the optimization problem. To that end, some embodiments lift thespecifications in a higher dimension, which can be obtained byintroducing additional variables and constraints in the optimizationproblem. As a result, the structure of the problem is retained, andstructure-exploiting optimization algorithms can be applied to reducethe computation time of the solution.

Additionally, or alternatively, some embodiments are based on therealization that the DMS can use the same optimization problem tomonitor the execution of the intermediate goals against unexpectedevents in the environment, such as newly appearing dangerous obstacles,unpredictable behavior from existing obstacles, and in the vehicle, suchas failures in the vehicle control systems, etc. By modifying theenvironment and vehicle prediction in the optimization problem, thepreviously computed solution can be checked against the newly modifiedenvironment and vehicle behavior to verify if the formal specificationrepresenting (i)-(iv) is still satisfied. As the decisions are fixed,and only the vehicle and obstacle predictions are adjusted, themonitoring can be performed faster than the decision in DMS. Hence themonitoring can be executed quickly and detect problems immediately whenthey occur, to promptly enable reactive measure such as the recomputingof the decision by DMS or emergency actions, such as stopping, driverintervention request, or warning signaling.

Accordingly, one embodiment discloses a control system for controlling amotion of a vehicle to a target driving goal in routing selectedaccording to a desired destination of the vehicle. The control systemincludes a memory configured to store a first model including one orcombination of a first motion model of the vehicle and a first trafficmodel of motion of a traffic in proximity of the vehicle and a secondmodel including a second motion model of the vehicle and a secondtraffic model of motion of the traffic, wherein the first model is anapproximation of the second model; and at least one processor coupledwith stored instructions implementing modules of the control system, themodules including: a decision-maker configured to determine a sequenceof intermediate goals leading to the next target goal by optimizing themotion of the vehicle subject to the first model and tightened drivingconstraints formed by tightening driving constraints by a safety margin,wherein the driving constraints include mixed logical inequalities oftemporal logic formulae specified by traffic rules and the routing,wherein the mixed logical inequalities define an area where the temporallogic formulae are satisfied, wherein the tightened driving constraintsshrink the area by the safety margin, and wherein the safety margin is afunction of a difference between the second model and the first model; amotion planner configured to determine a motion trajectory of thevehicle tracking the sequence of intermediate goals by optimizing themotion of the vehicle subject to the second model; and a controllerconfigured to generate and submit control commands to at least oneactuator of the vehicle to follow the motion trajectory.

Another embodiment discloses a method for controlling a motion of avehicle to a target driving goal in routing selected according to adesired destination of the vehicle, wherein the method uses a processorcoupled to a memory storing a first model including one or combinationof a first motion model of the vehicle and a first traffic model ofmotion of a traffic in proximity of the vehicle and a second modelincluding a second motion model of the vehicle and a second trafficmodel of motion of the traffic, wherein the first model is anapproximation of the second model, wherein the processor is coupled withstored instructions implementing the method, wherein the instructions,when executed by the processor carry out steps of the method, including:determining a sequence of intermediate goals leading to the next targetgoal by optimizing the motion of the vehicle subject to the first modeland tightened driving constraints formed by tightening drivingconstraints by a safety margin, wherein the driving constraints includemixed logical inequalities of temporal logic formulae specified bytraffic rules and the routing, wherein the mixed logical inequalitiesdefine an area where the temporal logic formulae are satisfied, whereinthe tightened driving constraints shrink the area by the safety margin,and wherein the safety margin is a function of a difference between thesecond model and the first model; determining a motion trajectory of thevehicle tracking the sequence of intermediate goals by optimizing themotion of the vehicle subject to the second model; and generating andsubmitting control commands to at least one actuator of the vehicle tofollow the motion trajectory.

Yet another embodiment discloses a non-transitory computer readablestorage medium embodied thereon a program executable by a processor forperforming a method, the method including: accessing a first modelincluding one or combination of a first motion model of the vehicle anda first traffic model of motion of a traffic in proximity of the vehicleand a second model including a second motion model of the vehicle and asecond traffic model of motion of the traffic, wherein the first modelis an approximation of the second model; determining a sequence ofintermediate goals leading to the next target goal by optimizing themotion of the vehicle subject to the first model and tightened drivingconstraints formed by tightening driving constraints by a safety margin,wherein the driving constraints include mixed logical inequalities oftemporal logic formulae specified by traffic rules and the routing,wherein the mixed logical inequalities define an area where the temporallogic formulae are satisfied, wherein the tightened driving constraintsshrink the area by the safety margin, and wherein the safety margin is afunction of a difference between the second model and the first model;determining a motion trajectory of the vehicle tracking the sequence ofintermediate goals by optimizing the motion of the vehicle subject tothe second model; and generating and submitting control commands to atleast one actuator of the vehicle to follow the motion trajectory.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic of a method for controlling a motion of avehicle according to some embodiments.

FIG. 2A is a schematic of a vehicle including a control unit employingprinciples of some embodiments of the present disclosure;

FIG. 2B is a block diagram of the control unit of FIG. 2A according tosome embodiments of the present disclosure;

FIG. 3 is a schematic of the layers of the control unit and monitoringsystem according to some embodiments of the present disclosure;

FIG. 4 illustrates a description of the routing information as used insome embodiments of the present disclosure in an exemplary trafficscene;

FIG. 5 illustrates a description of the specific intermediate goals asused in some embodiments of the present disclosure in the exemplarytraffic scene in FIG. 4;

FIG. 6 illustrates a description of the optional goals as used in someembodiments of the present disclosure in the exemplary traffic scene inFIG. 4;

FIG. 7 is a block diagram of the decision-making system as used in someembodiments of the present disclosure;

FIG. 8 is a flowchart of the operation of the decision-making system asused in some embodiments of the present disclosure;

FIG. 9 illustrate the effect of computing a sequence of goals based on afirst model of motion of the vehicle and then executing the goals in asecond first model of motion of the vehicle;

FIG. 10 illustrate the effect of robustness margin when computing asequence of goals based on a first model of motion of the vehicle andthen executing the goals in a second first model of motion of thevehicle;

FIG. 11A shows a block diagram and FIG. 11B shows pseudo code of anexemplar branch-and-bound optimization algorithm to solve MIP accordingto some embodiments.

FIG. 12 is a flowchart of the operation of the monitoring and reactivesystem as used in some embodiments.

DETAILED DESCRIPTION

FIG. 1 shows a schematic of a method for controlling a motion of avehicle according to some embodiments. The embodiments are based onrecognition that optimizing the motion of the vehicle is acomputationally expensive task due to high order of a motion model 180of the vehicle, versatility of the traffic, and the necessity togenerate the motion trajectory that satisfy the traffic rules 110applicable to the routing of the vehicle. Hence, some embodiments splitthe process of generation of the motion trajectory into decision making170 and motion planning 190. The objective of the decision-making is togenerate a sequence of decisions, referred herein as a sequence ofintermediate goals, such that if the vehicle tracks these intermediategoals, the mandate of traffic rules and routing would be satisfied andthe vehicle will eventually achieve the target driving goal. Hence, theconstrained optimization of the motion planner can be replaced withtracking decisions 190 produced by the decision maker 170.

Such a split allows to separate enforcement of the traffic rules fromthe enforcement of dynamics of the vehicle at the expense of providing aseparate decision making routine. Some embodiments are based on theunderstanding that such a routine can be programmed to enforce thetraffic rules. However, due to the variety of different traffic rulesapplicable in different situations, such a programming is problematic.To that end, some embodiments replace the traffic enforcement routinewith optimization 170. In the optimization 170, the traffic rules androuting are enforced on the optimization routine as driving constraints.Hence, the change of the traffic rules and routing would change theconstraints and not the optimization routine. In such a manner, anadaptive optimization of decision making for vehicle control indifferent traffic situations can be designed.

Notably, decision making generates a sequence of intermediate goals, notthe motion trajectory as a function of time. So, on one hand, thecomputational burden on optimized decision making combined with motiontracking is still preferable over optimized motion trajectorygeneration. On the other hand, the computational burden of such acombination is still problematic for some embedded processors currentlyused in some autonomous vehicles.

To that end, some embodiments approximate 160 the motion model of thevehicle 180 used for motion planning Such an approximated motion model160 is referred herein as a first motion model 160, while the motionmodel 180 used for motion planning is referred herein as a second motionmodel 180. Hence, the first motion model is an approximation of thesecond motion model, such that an order of the second motion model 180is higher than an order of the first motion model 160 or a computationalcomplexity of the functions of the second motion model 180 is higherthan a computational complexity of the functions first motion model 160.

The approximation allows to reduce the computational burden of thedecision making, however, can lead into an accuracy of tracking thedecisions due to the differences in the models. To address this problem,some embodiments optimize the decision making not subject to the drivingconstraints 130 specified by the traffic rules 110, but subject to thetightened driving constraints 150, which are the driving constraints 130tightened by a safety margin 140. In some embodiments, the safety margin140 depends, i.e., is a function of a difference between the secondmotion model and the first motion model. For example, in one embodiment,the safety margin 140 is selected such that for all states of thevehicle satisfying the tightened driving constraints 150 there is acontrol input that transition the state of the vehicle according to thesecond motion model without violating the driving constraints 130. Insuch a manner, the tightened driving constraints 130 allow to balancethe approximation of the motion model of the vehicle.

In addition, some embodiments are based on realization that the trafficrules can be represented by temporal logic formulae, which can beautomatically transformed into driving constraints. Specifically, thetemporal logic formulas can be selected from a database of signaltemporal logic (STL) specifications based on a current state of thevehicle, a current state of a traffic and the next target location andautomatically converted into mixed logical inequalities defining an areawhere the temporal logic formulae are satisfied. Having the safetymargin determined to represent the difference in motion modelapproximation, the tightening of the driving constraints just shrinksthat area by an amount related to the safety margin and the formula towhich such margin is applied. In such a manner, the generating of thetightened driving constraints is simplified.

Hence, according to some embodiments, a control system for controlling amotion of a vehicle to a next target goal in routing selected accordingto a desired destination of the vehicle uses a first motion model 160 ofthe vehicle, a second motion model 180 of the vehicle, a decision-maker170 configured to determine a sequence of intermediate goals leading tothe next target goal, and a motion planner 180 configured to determine amotion trajectory of the vehicle tracking the sequence of intermediategoals.

The decision-maker 170 is configured to determine a sequence ofintermediate goals leading to the next target goal by optimizing themotion of the vehicle subject to the first motion model 160 andtightened driving constraints 150 formed by tightening drivingconstraints by a safety margin 140. The driving constraints includemixed logical inequalities of temporal logic formulae 120 specified bytraffic rules and the routing 110. The mixed logical inequalities definean area where the temporal logic formulae are satisfied, and thetightened driving constraints shrink the area by the safety margin 140,which is a function of a difference between the second motion model 180and the first motion model 160 and the type of formulae to which themargin is applied.

The motion planner 190 is configured to determine a motion trajectory ofthe vehicle tracking the sequence of intermediate goals by optimizingthe motion of the vehicle subject to the second motion model 180. Thecontrol system is further configured to generate and submit controlcommands to at least one actuator of the vehicle to follow the motiontrajectory.

FIG. 2A is a schematic of a vehicle including a control unit employingprinciples of some embodiments of the present disclosure. For example,FIG. 2A shows a schematic of a vehicle 211 including a control unit 212employing principles of some embodiments of the present disclosure. Asused herein, the vehicle 211 can be any type of wheeled vehicle, such asa passenger car, bus, or rover. Also, the vehicle 211 can be anautonomous or semi-autonomous vehicle. For example, some embodimentscontrol the motion of the vehicle 211. Examples of the motion includelateral motion of the vehicle controlled by a steering system 213 of thevehicle 211. The steering system 213 is controlled by the controller212.

The vehicle can also include an engine 216, which can be controlled bythe controller 212 or by other components of the vehicle 211. Thevehicle 211 can also include one or more sensors 215 to sense, bynon-limiting example, its current motion quantities and internal status.Examples of the sensors 215 can include global positioning system (GPS),accelerometers, inertial measurement units, gyroscopes, shaft rotationalsensors, torque sensors, deflection sensors, pressure sensor, and flowsensors. The vehicle can be equipped with a transceiver 217 enablingcommunication capabilities of the controller 212 through wirelesscommunication channels via an input interface 218. The vehicle can alsoinclude one or more other sensors 214 a, 214 b to sense the surroundingenvironment. Examples of the sensors 214 a, 214 b can include distancerange finders, radars, lidars, and cameras. Alternatively, informationabout the surrounding environment can be received through thetransceiver 217. The vehicle is equipped with map database system thatstores information about the road in the area where the vehicleoperates, or it can access map information stored remotely through thetransceiver 217.

FIG. 2B is a block diagram of the control unit of FIG. 2A according tosome embodiments of the present disclosure. For example, FIG. 2 shows ablock diagram of the control unit 212 according to one embodiment of thepresent disclosure. The controller 212 includes a hardware processor 201connected to a memory 202, e.g., a non-transitory computer readablemedium. In some implementations, the memory 202 includes a first section211 for storing information about the vehicle and a second section 212for storing a program for controlling the vehicle, a third section 213for storing driving map data, and a fourth section 214 for storingmotion models of the traffic.

For example, the first section 211 of the memory 202 can storeparameters for the behavior of the vehicles, such as maximumacceleration, steering, and steering rate, as well as store a firstmodel of motion of the vehicle and a second model of the motion of thevehicle. In various embodiments, the number and complexity of equationsdescribing the second model of motion of the vehicle is higher that thenumber and complexity of equations describing the first model of motionof the vehicle. Also, for example, the fourth section 214 of the memory202 can store a first model of motion of the traffic and a second modelof the motion of the traffic.

Still referring to FIG. 2B, in various embodiments, the number andcomplexity of equations describing the second model of motion of thetraffic is higher that the number and complexity of equations describingthe first model of motion of the traffic. Those embodiments are based onrecognition of the necessity to use different motion models for checkingwhat intermediate objectives the vehicle may be able to achieve in thenear future, and for generating the trajectory and for controlling thevehicle according to such a trajectory. For example, in order to checkif the vehicle is capable of achieving a sequence of goals, a longfuture horizon needs to be considered. Having a high order physicalmodel to compute the motion of the vehicle over the extended futurehorizon is computationally difficult. Conversely, when the immediategoal is known, the control of the vehicle according to the desiredtrajectory can consider only a short future horizon. To that end, insome embodiments, the controller 212 determines the next goal using thefirst, i.e., low order motion model, while planning and control uses atleast a second, i.e., higher order, motion model.

The second section 212 of the memory 202 can have embodied thereon aprogram executable by the processor 201 for performing a method forcontrolling the vehicle 211.

Still referring to FIG. 2B, the third section 213 of the memory 202includes map information, such as addresses and road networks, and itmay also include additional information such as intersections, stop andtraffic light locations, number and position of lanes, speed limit,traffic rules, etc. The map information may be stored already in thethird section of the memory 213 when the vehicle starts driving, oralternatively, this information is made available to the control unit bythe communication transceiver 217 and the environment sensors 214 a, 214b.

The processor 201 can be any computational device capable of performingcomputations, and can include one or many physical devices of the sameor of different types. It is possible that the processor 201 can includemultiple computational devices, e.g., microprocessors. Similarly, thememory 202 can be any logical memory and/or non-transitory computerreadable storage medium capable of storing information, and can includeone or more physical information storage means, of the same or ofdifferent types. The computations performed by the processor 201 arecommanded by the program stored in the second section of the memory 212,and use the vehicle information stored in the first section of thememory 211, the information about the map stored in the second sectionof the memory 213, the information about the vehicle 211 obtained fromthe sensors 215, the information of the environment 203 obtained fromthe sensors 214 a, 214 b. The computation of the processor 201 resultsin commands 204 that change the motion of the vehicle.

Still referring to FIG. 2B, the program executed by the processor 201enables autonomous driving (AD) of the vehicle 211, where here AD isintended to include also semi-autonomous driving. During this operation,the program executed by the processor 201 aims at achieving a specificoverall objective of driving, such as reaching a specific location. Theoverall objective is achieved by appropriately influencing the motion ofthe vehicle 211. The software program executed by the processor 201 canlogically be separated into multiple modules. For example, in oneembodiment, the program executed by the processor includes at least twomodules arranged in a sequence as layers such that output of one layeris an input to a next layer. As used herein, such layering specifieslayers or logical modules of the control unit 212, and allows separatingthe control into different stages requiring different information.

FIG. 3 shows a schematic of the layers of the control unit according toone embodiment of the present disclosure. In this embodiment, thecontrol unit 212 includes three layers of the control. The informationabout the state of the vehicle and of the obstacles in the dynamicenvironment from sensors and estimators is provided 307 to the differentlayers. The Routing 301 uses the static map information stored in thethird section of the memory 213 of FIG. 2 and the current position ofthe vehicle obtained from sensors 214 a, 214 b to determine a sequenceof roads in the road network that the vehicle traverses from its currentposition to reach its final destination. The final destination can beprovided for instance by the user. The Routing module can be implementedby a Car Navigation system. The decision-maker or Decision Making module302 implements the DMS that uses information from the current state ofthe vehicle, from at least a part of the sequence of roads in the roadnetwork that the vehicle traverses from its current position to reachits final destination, and of the dynamic environment to determines asequence of one or more intermediate goals and provide them to thePlanning and Control module 303. Upon receiving the sequence of goals,the motion-planner or motion planning module 304 which implement the MPSwithin the Planning and Control module 303 computes a trajectory forachieving the sequence of goals determined by the DMS. The VehicleControl module 305 determines commands of the vehicle actuators, such assteering, acceleration, deceleration, that modify the vehicle behaviorso that the vehicle achieves an actual trajectory as close as possibleto the current trajectory provided by the planning and control module.The commands to the vehicle actuators are then received by the ActuatorControl sub-module 306 that modifies the control signals to theactuators, such as electric motor voltage, throttle opening, brake padspressure, to achieve the desired vehicle commands.

In parallel to the planning stack, a Monitoring and Reactive modulecompares the decisions that have been made by the Decision Making modulewith the information on the state of the vehicle and of the obstacles inthe dynamic environment from sensors and estimators 307, to ensurecorrect operation of the vehicle according to the determined sequence ofone or more intermediate goals provided to the Planning and Controlmodule 303, and if anomalies or potential errors are detected, providesinformation to the Decision Making module and the submodules on thePlanning and Control module on the anomaly and indications on correctiveactions.

FIG. 4 illustrates a description of the routing information as used insome embodiments of the present disclosure in an exemplary trafficscene. For example, FIG. 4 depicts a scenario with the vehicle undercontrol, referred to as ego vehicle 411, with the traffic composed ofother vehicles shown similar to 412, lanes marked for instance 413 asL6, stop lines marked for instance 414 as S1, intersections marked forinstance 415 as I3. With reference to FIG. 4, for the vehicle inposition 401, with final destination 402, the Routing 301 provides thesequence of roads indicated by arrows 403, and the sequence of turnsindicated by arrows 404. It should be noted however that the sequence ofroads 403 and the sequence of turns 404 does not by itself specify atrajectory or a path for the vehicle. There are a number of discretedecisions to take such as in what lane the vehicle is to drive, if thevehicle should change lane or stay in the current lane, if the vehicleshould start decelerating to stop at the stop line or not, if thevehicle is allowed to cross the intersection, and so on. Furthermore,there are a number of continuous decisions to make, such as the timedsequence of positions and orientations that the vehicle should achieveon the travel from its initial point to its destination. These decisionscannot be taken by the Routing 301 because they depend on the currenttraffic at the moment when the vehicle reaches the correspondinglocation, which is in general unknown to the Routing due to theuncertainty of traffic motion and uncertainty of the moment at which thevehicle will reach the location.

The actual trajectory, in terms of sequence of positions andorientations and corresponding time instant, that the vehicle shouldexecute to get to the final destination is usually determined by aplanning and control module 303. However, the planning and control 303of FIG. 3 may not be able to operate based directly on the informationprovided by Routing 301. In particular, operating discrete andcontinuous decision in a single step leads to a so-called hybriddecision problem, that is a problem with both discrete decisions (inwhich lane to drive, whether to pass or follow a vehicle, etc.) andcontinuous decisions (the ego vehicle velocity, the steering angle,etc), which based on experimentation and computing theory resultsrequires a very large amount of computations. Instead, the computingunit 212 has often limited memory and processing speed, and hence it isbeneficial to decompose the problem in a way that makes itcomputationally tractable, yet it ensures that no inconsistencies arecaused by the decomposition. That is, decomposing the overall probleminto many simpler subproblems, solving each single subproblem insequence, and operating according to the sequential solution of thesubproblems, results in a solution to the overall problem.

Still referring to FIG. 4, another realization of the present disclosureis that one can decompose the problem in terms of discrete decisions andcontinuous decisions where a decision-making module 302 of FIG. 3operates discrete decisions, such as whether to change lane or stay inthe current lane, whether to start decelerating to stop at the stop lineor not, whether to cross the intersection or not, and converts this intointermediate goals for the Planning and Control module 303 of FIG. 3.The Planning and Control module 303 receives the current intermediategoal and possibly additional parameters for adjusting its computation tothe current intermediate goal from the decision-making module 302, andperforms its computation. The planning and control module may inform thedecision-making module of the achievement of the current intermediategoal, or the impossibility of achieving the current intermediate goal.The goals provided by the decision-making module 302 should beachievable by the Planning and Control module, according to the currenttraffic conditions and vehicle conditions, should ensure that thesequence of intermediate goals allows to be interconnected, i.e., theplanner can switch from one goal to the next one, and achieving allintermediate goals results in achieving the overall goal, i.e., reachingthe final position.

Thus, the decision-making module 302 of FIG. 3 processes the informationfrom Routing 301 using the map stored in the third section of the memory213 of FIG. 2 to produce a sequence of goals, and, using informationfrom sensors and communication 214 a, 214 b selects one or morealternative current goals to provide to the Planning and Control module303 of FIG. 3, which uses those goals to determine and execute thecurrent trajectory.

Still referring to FIG. 4, it is further realization of this presentdisclosure that some intermediate goals are specific and some othergoals are optional. The road segments indicated by Routing 301 of FIG. 3determines specific goals, such as specific turns at intersections.However, there are additional specific goals due to the proper operationof the vehicle according to driving rules. For instance, staying stoppedat a stop line, and also decelerating to stop at a stop line, isspecific according to driving rules. Similarly, to stay on a specificlane at a specific intersection based on the turn to be taken at suchintersection may be mandatory. The same can be said as regards being ona specific lane before exiting the general road.

FIG. 5 illustrates a description of the specific intermediate goals asused in some embodiments of the present disclosure in the exemplarytraffic scene in FIG. 4. For example, in FIG. 5, this results inspecific intermediate goals 501, 502, 503, which are related to beingstopped at a stop line. While specific intermediate goals 501 and 502require a specific lane, intermediate goal 503 does not. Specificintermediate goal 504 is related to being in a specific lane beforeexiting the general road, and specific intermediate goal 505 coincideswith the final destination, i.e., the final goal.

FIG. 6 illustrates a description of the optional intermediate goals asused in some embodiments of the present disclosure in the exemplarytraffic scene in FIG. 4. Besides specific intermediate goals, there area number of intermediate goals that are optional. For instance, in FIG.6 trajectories 603 and 604 both reach the specific intermediate goal503, yet trajectory 603 has intermediate goals 606 and 607 that prompt 2lane changes, while trajectory 604 does not. Both trajectories 603, 604have intermediate goals 608, 609 of changing lane before the stopline,which is also not required since both lanes are allowed to proceedforward at intersection 14. In fact, trajectory 605 has no intermediategoals and directly reaches the specific goal 503. Also, besides thesequence of intermediate goals, the timing of those can be different, astrajectories 601,602 both have intermediate goals 611, 612 of a lanechange to L2, which is necessary due to the specific intermediate goalof stopping in lane L2 at stop line S1 to turn left at intersection I1,yet the location where the intermediate goals 611, 612 are applied aresignificantly different.

Some embodiments are based on the understanding that the selection ofthe intermediate goals can be performed based on graph searchingtechniques. For example, to address the connection between Routingmodule and path planning module by a DMS it is possible to construct agraph of intermediate goals from the Routing module information and fromthe traffic rules information and then uses vehicle and obstacleinformation together with the graph to determine at each instant thenext intermediate goal that is achievable by the vehicle without causingcollision with traffic or violating traffic rules, and from which thevehicle is still guaranteed to be able to achieve the final goal.However, the design of the graph is particularly complicated because itrequires the translation of natural language descriptions into graphstates and connections, for instance of the traffic rules.

To that end, some embodiments are based on the realization that ratherthan converting the traffic rules and the routing information into agraph of intermediate goals, one can instead describe such informationin terms of a temporal logic-based formal specification language, suchas linear temporal logic (LTL) or signal temporal logic (STL), fromwhich the graph of intermediate goals is automatically generated, withthe advantage of an easier conversion from natural language to formalspecification language.

Signal Temporal Logic (STL) Specifications

In signal temporal logic, regions of physical states of the vehicles andof the traffic models are associated to predicates Π={π^(μ1), π^(μ2), .. . } by functions μ_(i):

→

where

is the set of vehicle and traffic states. An STL formula ϕ is definedrecursively by

ϕ:=π^(μ)|¬ϕ|ϕ₁Λϕ₂|ϕ₁

ϕ₂   (1)

where ϕ₁, ϕ₂, are also STL formulae defined according to (1), ¬, Λ,

represent the logical operators “not”, “and”, and the temporal operator“until”, respectively. Temporal operator “until” is equipped with aninterval I, indicating the time window in which the STL formula isevaluated. A number of additional operators can be derived from the onesin (1) such as logical “or”ϕ₁∨ϕ₂≐¬(¬ϕ₁Λ¬ϕ₂), temporal “eventually”⋄_(I)ϕ₁≐T

_(I)ϕ₁, and temporal “always” □ϕ≐¬(⋄¬ϕ), where eventually indicates thatsooner or later the argument is true, always indicates that the argumentis always true, and T denotes a predicate that is always true, and“next” ◯ϕ≐(T

_([1,1])∅).

We say that an STL formula ϕ is satisfied by a trajectory ξ={x₀, x₁, . .. } of combined vehicle and traffic states at time step t, denoted as ξ,t|=ϕ according to the following rules

ξ,t

T,

ξ, t

π^(μ) if and only if μ(x_(t))>0,

ξ, t

¬ϕ if and only if ξ, t

ϕ,

ξ, t

ϕ₁Λϕ₂ if and only if ξ, t

ϕ₁ and ξ, t

ϕ₂,

ξ, t

ϕ₁

_([a,b])ϕ₂ if and only if there exists t₂ ∈[t+a, t+b] such that ξ, t₂

ϕ₂ξ, t₁ϕ₁ for t₁ ∈[t, t₂].   (2)

where similar definitions can be obtained for derived operators, such as“or”, “eventually”, “always”. A quantitative scoring of the STL formulasatisfaction can be obtained by introducing a measure for the formulasatisfaction ρ(ϕ, ξ, t) called robustness score and computed as

ρ(μ, ξ,t)=μ(x(t)),

ρ(¬ϕ, ξ,t)=−ρ(ϕ, ξ,t),

ρ(ϕ₁Λϕ₂, ξ, t)=min(ρ(ϕ₁, ξ, t), ρ(ϕ₂, ξ, t)),

ρ(ϕ₁

_(I)ϕ₂, ξ, t)=max_(t) ₂ _(-t) _(∈) _(I) min (ρ(ϕ₂, ξ, t₂), min_(t) ₁_(∈[t, t) ₂ _(])ρ(ϕ₁, ξ, t_(i))).   (3)

where the formula is satisfied when ϕ(ϕ, ξ, t)>0. The sign of therobustness score indicates if the specifications are satisfied orviolated, whereas the absolute value indicates quantitively how muchthat happened.

Some embodiments formulate traffic rules by STL formulae. Consider, forinstance, the following list of formulas

in_lane ∨(lane_changing

_([1.5,4.5)] in_lane)

□safety_distance_ahead

(¬intersection) ∨(intersection Λ((red_light Λvehicle_stop)

(¬red_light Λcrossing)))

¬(red_light Λ◯-red_light) ∨((red_light Λ◯-red_light) Λ⋄_([0,3])crossing)   (4)

The first formula specifies proper operation of the vehicle in the lane,namely, that either the vehicle is in the lane, or it is lane changinguntil it goes back into the lane within 1.5s and 4.5s from the beginningof the lane change. The second formula specifies to always maintain asafety distance from the preceding vehicle. The third formula specifiesbehavior in the intersection, where in presence of a red light, thevehicle must stop until the light is no longer red and the vehiclestarts moving again. The fourth formula specifies that when the lightturns from red to green, the vehicle must start crossing theintersection within 1 to 3 seconds.

Similarly, the specific intermediate goals and the final goal from therouting module can be specified by STL rules, such as

⋄_([t) _(i) _(,t) _(i+1) _(]) achieve_int_goal_(i) , i=1, . . . , n _(g)  (5)

where n_(g) is the number of specific intermediate mandatory goals fromthe routing module and t_(i)<t_(i+1), that specifies that every specificintermediate goal must be satisfied in finite time, each after theprevious one, and such as

achieve_goal₃Λ◯(crossing

_([1,10]) turn_left)   (6)

that specifies that after achieving goal number 3, the vehicle crossesan intersection and makes a left turn, within 1 to 10 seconds. Thespecification of achieving the final goal, i.e., the completion of thetrip, can be formulated as

⋄_([0,T) _(max) _(]) achieve_final_goal   (7)

where T_(max) indicates the maximum travel time.

Thus, the traffic rules and specific intermediate goals can be specifiedby the set of STL formulae

{ϕ^(i)}_(i=1) ^(n) ^(ϕ)   (8)

The predicates are connected to vehicle and traffic states, containingat least positions and velocities of the vehicle and the traffic, byinequalities describing the region of the combined state space where thepredicates are true. For instance,

$\begin{matrix}\left( {{achieve\_ final}{\_ goal}\left. \left. {= T} \right)\Leftrightarrow\left( {{{H_{g}\ \begin{bmatrix}p_{x}^{v} \\p_{y}^{v}\end{bmatrix}} \leq K_{g}},{v_{v} \leq 5}} \right) \right.} \right. & (9)\end{matrix}$

indicates that the predicate describing acceptance of the final goal istrue if and only if the vehicle velocity is below 5 km/h and theposition of the vehicle satisfies the linear inequalities describing thelocation of the trip destination. Also, the function ,u determines themargin of satisfaction of the predicate at time t for trajectory alsocalled robustness score, by

$\begin{matrix}{{\mu\left( {{{achieve}_{-}{final}_{-}{goal}},\xi,t} \right)} = {\min\left( {{K_{g} - {H_{g}\begin{bmatrix}{p_{x}^{v}(t)} \\{p_{y}^{v}(t)}\end{bmatrix}}_{i}},{5 - {v_{v}(t)}}} \right)}} & (10)\end{matrix}$

The robustness score of complex formulae can be computed from those ofpredicates by operations such as

ρ(μ, ξ,t)=μ(x(t)),

ρ(¬ϕ, ξ, t)=−ρ(ϕ, ξ, t),

ρ(ϕ₁Λϕ₂ , ξ, t)=min(ρ(ϕ₁ , ξ, t), ρ(ϕ₂ , ξ, t)),

ρ(ϕ₁

_(I)ϕ₂ , ξ, t)=max_(t) ₂ _(-t) _(∈) _(I) min (ρ(ϕ₂ , ξ, t ₂), min_(t) ₁_(∈[t, t) ₂ _(])ρ(ϕ₁ , ξ, t ₁)).   (11)

The robustness scores determine how much the actual behavior can bedifferent from the expected behavior without changing the validity ofthe formulae.

Mixed Integer Constraints

For executing computations in real-time with a dynamic environment theSTL specifications can be converted into mixed logical inequalities byintroducing Boolean variables. For instance, it is possible to introduceone Boolean variable per each predicate defined by the mixed integerinequalities

Mz(t)^(μ)>μ(π^(μ) , ξ, t)

M(1-z(t)^(μ))>-μ(π^(μ) , ξ, t)   (12)

which ensures that z(t)=1 if and only if μ(π^(μ), ξ, τ)>0. Then, the STLformulas can be translated into logical constraints on the Booleanvariables z. For instance,

z ₂ =¬z ₁ ↔z ₂=1−z ₁

z ₃ =z ₁ Λz ₂ ↔z ₃ ≤z ₁ , z ₃ ≤z ₂ , z ₃ ≥z ₁ +z ₂−1

z ₃ =z ₁ ∨z ₂ ↔z ₃ ≥z ₁ , z ₃ ≥z ₂ , z ₃ ≤z ₁ +z ₂   (13)

and the temporal operators can be translated into integer constraints onsequences of variables z over time. For instance

$\begin{matrix}{{\left. {\bullet_{\lbrack{a,b}\rbrack}\phi_{t}}\leftrightarrow \right.\underset{t = a}{\overset{b}{⩓}}{{\mathcal{z}}^{\phi}(t)}}{\left. {\Diamond_{\lbrack{a,b}\rbrack}\phi_{t}}\leftrightarrow \right.\underset{t = a}{\overset{b}{⩔}}{{\mathcal{z}}^{\phi}(t)}}} & (14)\end{matrix}$

It is important to notice that while the translation of logical operatorin (13) involves variables all associated to the same time instant, thetranslation of temporal operators in (14) in general involves variablesassociated to different time instants.

As a consequence, the STL formulae in (9) specifying the traffic rulesand goals for the vehicle can be converted into a set of mixed integerinequalities between a sequence of vehicle and traffic states over timeand the vector of the introduced Boolean variables z

$\begin{matrix}{{{{\rho\left( {\phi^{i},\xi,t} \right)} = {\rho^{i} \leq {{\overset{N}{\sum\limits_{t = 0}}{H_{b}^{i}{{\mathcal{z}}(t)}}} + {H_{r}^{i}{x(t)}}}}},{i \in \mathcal{I}_{h} \subseteq \left\{ {1,\ldots\mspace{14mu},\ n_{\phi}} \right\}}}{{{\rho\left( {\phi,\xi,t} \right)} = {\rho \leq {\rho\left( {\phi^{i},\xi,t} \right)}}},{i \in \mathcal{I}_{h}}}} & \left( {15a} \right) \\{{\rho\left( {\phi,\xi,t} \right)} = {\rho \geq ɛ > 0}} & \left( {15b} \right)\end{matrix}$

where ε is an infinitesimally small positive constant, e.g., in therange of the processor precision and N is the prediction horizon uponwhich the formulae is evaluated and ρ is computed as the overallrobustness score for the satisfaction of the formulae from (11).

As a consequence, one embodiment can include constraints on the overallrobustness score p to ensure that the overall behavior admits a certainamount of difference between the actual and expected behavior

ρ≥R≥ε>0   (15c)

Vehicle Motion Model for DMS and MPS

In some embodiments, in order to keep the computation feasible inreal-time, different models of vehicle motion are used in the DMS andMPS. The DMS performs decisions based on predictions of vehicle motionfor longer in the future, but more coarsely. The MPS plans the vehiclemotion for shorter period in the future, but more finely, since itrequires higher precision so that the planned vehicle motion can beexecuted by the vehicle. Thus, some embodiments use a first vehiclemodel in DMS and a second vehicle model in MPS. However, it is importantto ensure consistency of the predictions of the two models, and inparticular that if the DMS finds a solution to the decision makingproblem that satisfies the problem objectives according to the first(coarse) model of vehicle motion, it is guaranteed that a solution forthe planning problem of MPS exists, according to the second (fine) modelof vehicle motion to find a solution

In some embodiments, the first model of vehicle motion,

x ₁(t+1)=f ₁(x ₁(t), μ₁(t))   (16)

is used in Decision Making 303 for coarse predictions to select whichspecific intermediate goals can be achieved by the vehicle. In variousimplementations, this model is coarser, lower complexity and/or hasfewer parameters than the second model of the vehicle motion, because itneeds to predict longer in the future and hence it is necessary that itmakes fewer calculations for each prediction.

For instance, some embodiments of this present disclosure use as firstmodel of the vehicle motion (16) a discrete time linear model withsampling period T_(s), which has state x₁=(p_(x), p_(y), v_(x)), where(p_(x), p_(y)) is the position vector with respect to a non-movingCartesian coordinate frame, and v_(x) is the vehicle longitudinal speed,and has input μ₁=(a, v_(y)) where a is the acceleration and v_(y) is thelateral velocity,

p _(x)(t+1)=p _(x)(t)+v _(x)(t)T _(s)

p _(y)(t+1)=p _(y)(t)+v _(y) (t)T _(s)

v _(x)(t+1)=v _(x)(t)+a _(x)(t)T _(s)   (17)

To which one can add the constraint v_(y)(t)≤a|v_(x)(t)| to ensureappropriate relation between vehicle longitudinal and lateral motion.

In some embodiments, the second model of vehicle motion

x ₂(t+1)=f ₂(x ₂(t), μ₂(t))   (18)

is used in the Motion Planning module 304 to compute the vehicletrajectory that actually achieves the goal determined by Decision Making303. Since the trajectory computed by the Motion Planning module 304 isactually executed by the vehicle in order to achieve the goal, the modelof vehicle motion used by the motion planning module 304 needs to bemore precise, and hence has at least one among higher order, moreparameters and more complicated equations. However, since the predictionof the Motion Planning module 304 is usually shorter than the one of thedecision making, the higher order model is still feasible in terms ofcomputations required.

For instance, some embodiments of this present disclosure use as secondmodel of the vehicle motion (4) the kinematic bicycle model which hasstate x₂=(p_(x), p_(y), v_(x), θ, δ), where (p_(x), p_(y)) is theposition vector with respect to a non-moving Cartesian coordinate frame,and v_(x) is the vehicle longitudinal speed, v_(y) is the lateralvelocity, θ is the heading, and δ is the steering angle, inputu₂=(u_(a), u_(δ)) where u_(a) is the acceleration and u_(δ) is thechange in steering angle,

$\begin{matrix}{{{p_{x}\left( {t + 1} \right)} = {{p_{x}(t)} + {T_{s}^{(2)}{v_{x}(t)}\frac{\cos\left( {{\psi(t)} + {\beta(t)}} \right)}{\cos\left( {\beta(t)} \right)}}}}{{p_{y}\left( {t + 1} \right)} = {{p_{y}(t)} + {T_{s}^{(2)}v_{x}\frac{\sin\left( {{\psi(t)} + {\beta(t)}} \right)}{\cos\left( {\beta(t)} \right)}}}}{{\theta\left( {t + 1} \right)} = {{\theta(t)} + {T_{s}^{(2)}{v_{x}(t)}\frac{\tan\left( {\delta(t)} \right)}{L}}}}{{v_{x}\left( {t + 1} \right)} = {{v_{x}(t)} + {T_{s}^{(2)}u_{a}}}}{{\delta\left( {t + 1} \right)} = {{\delta(t)} + {T_{s}^{(2)}u_{\delta}}}}} & (19)\end{matrix}$

where L is the wheel base, L=l_(f)+l_(r), l_(f) and l_(r) are the frontand rear axles distances from the vehicle center of mass, β=arctan(l_(r) tan(δ)/L) is the body-slip angle, and T_(s) ⁽²⁾ is the samplingperiod of the second model of the vehicle motion where in general T_(s)⁽²⁾≤T_(s).Constraints on inputs of Models of Vehicle Motion

Some embodiments, for computing the vehicle trajectories account forconstraints on the states and inputs of the vehicle models. Suchconstraints are determined by the allowed range of actuators, such asminimum and maximum steering angle, angular rate, acceleration andbraking, legal and safety requirements, such as minimum and maximumvelocity. The constraints result in bounds to the state and inputvectors for the first motion model

(x_(v), u_(v)) ∈

  (20)

which for instance include the constraint v_(y)(t)≤a|v_(x)(t)| thatensure a proper relation between longitudinal and lateral velocity, andfor the second motion model

(x₁, u₁)∈

  (21)

Which should be satisfied by the decision and planning algorithmsoperating on the models.

Difference between First and Second Motion Models

Some embodiments compute an envelope to ensure the consistency of thefirst and second motion models, that is, to ensure that once atrajectory of the state of the first model of vehicle motion (16) thatsatisfies the constraints (20) is found for achieving a goal, thereexists a trajectory of the state of the second model of vehicle motion(18) that satisfies the constraints (21) is found that achieves the samegoal.

To this end the DMS is provided with a set W, such that for all statesof the second model of the vehicle motion x₂ that satisfies (21) forsome input u₂, and for all x₁=P(x₂), u₁ satisfying (20) where P is apre-defined transformation that associates a state of the first model ofthe vehicle motion that satisfies to a state of the second model, thereexists an input u₂ that satisfy (21) together with x₂, such that

(f₁(P(x₂)+w, u₁) −P(f₂(x₂, u₂)))∈W, ∀w∈W   (22)

that is, the difference between the update according to the first modelwith input u₁ of the transformation of the state of the second modelplus any disturbance in W, and the projection of the update according tothe function of the second model with input u₂ of the state of thesecond model is within W. In such a manner, wherein the safety margin isselected such that for all states of the vehicle satisfying thetightened driving constraints according to the first motion model of thevehicle, there is a control input that transition the state of thevehicle according to the second motion model without violating thedriving constraints

An example for P is the projection operator on a specific subspace ofthe space of x₂. According to (22) it is always possible to maintain thedifference between prediction with high precision model and that withlow precision model

within the error set W. In some embodiments, the set W is function ofthe state of the first model of motion of the vehicle, W(x₁).

Traffic Models

In some embodiments of the present disclosure, DMS 302 and Planning andControl 303 use a first model of traffic motion and a second model oftraffic motion stored in the first section 211 of the memory 202 topredict the future behavior of other vehicles present in the road, wherethe first model of the traffic motion is simpler to evaluate, in termsof computations, than the second model of the traffic motion.

The state of a traffic according to the first and second model oftraffic motion x_(t1), x_(t2) is obtained by combining the states of alltraffic vehicles on the road in the area where the vehicle under controlis currently located

x _(ti)=(x _(ti) ⁽¹⁾ , . . . , x _(ti) ^((N) ^(T) ⁾), i=1, 2   (23)

where, for instance, x_(t1) ⁽¹⁾ is the state of the first trafficvehicle according to the first model of the traffic motion, and N_(T) isthe number of total vehicles in traffic. The first model of the trafficmotion describes the motion of each vehicle in traffic according to afirst equation

x _(t1) ^((i))(t+1)=f _(t1)(x _(t1) ^((i))(t))   (24)

The second model of the traffic motion describes the motion of eachvehicle in traffic according to a second equation

x _(t2) ^((i))(t+1)=f _(t2)(x _(t2) ^((i))(t))   (25)

In some embodiments of the present inventions, a set W_(t) is chosen tosatisfy

(f _(t1) P(x _(t1))+w)−P(f _(t2)(x _(t2))))∈W _(t) , ∀w ∈W _(t)   (26)

ensuring a proper margin between traffic motion predicted with first andsecond model.

The control unit 212 receives information about the traffic state fromsensors and communication 214 a, 214 b. The equations (10), (11) can bespecified by any standard vehicle model such as the unicycle model (2)or the kinematic bicycle model (4).

Motion Model Formulation as Constraints

Some embodiments are based on realization that if discrete-time linearmodels such as (17) are used as motion model for vehicle and traffic,and if the feasible set of the constraints (20), (21) are polyhedral,the motion model and the constraints can be formulated asblock-structured linear constraints

$\begin{matrix}{{{{x_{1}\left( {t + 1} \right)} - {A_{1}{x_{1}(t)}}} = {B_{1}{u_{1}(t)}}}{{{{x_{t1}^{(i)}\left( {t + 1} \right)} - {A_{t\; 1}^{(i)}{x_{t\; 1}^{(i)}(t)}}} = 0},{{\forall i} = 1},{\ldots\mspace{14mu} N_{T}}}{{{H_{x}{x_{1}(t)}} + {H_{v}{u_{1}(t)}} + {\sum\limits_{i = 1}^{N_{T}}{H_{t1}^{(i)}{x_{t1}^{i}(t)}}}} \leq K}} & (27)\end{matrix}$

where each inequality involves variables from the same sampling instantsor maximum from two consecutive sampling instants.

Indeed, the inequalities in (27) may be compressed by removingimplicitly defined variables and equality constraints resulting in asingle set of constraints dependent only on the initial state of vehicleand traffic, and on the inputs to the vehicle

$\begin{matrix}{{\sum\limits_{t = 0}^{N}{H_{u}^{c}{u_{1}(t)}}} \leq {K + {H_{x}^{c}{x_{1}(0)}} + {\sum\limits_{i = 1}^{N_{T}}{H_{t\; 1}^{i}{{{}_{\;}^{}{}_{t\; 1}^{}}(0)}}}}} & (28)\end{matrix}$

Decision Making with STL Specification as MIP Problem

In some embodiments, the DMS is implemented by solving a mixed integerprogramming (MIP) problem by combining the mixed integer constraintformulation of the STL specifications of traffic rules and driving goals(15), the first motion model for vehicle and traffic expressed as linearconstraints (27), constraints that relates to the robustness score ofthe STL specification satisfaction and a cost function involving therobustness score and the performance of the vehicle motion according tothe first vehicle motion model,

$\begin{matrix}{{{\min\limits_{{\{{({{x{(t)}},{u_{1}{(t)}},{{\mathcal{z}}{(t)}}})}\}}_{t},\rho,{\{\rho^{j}\}}_{j}}{J_{p}\left( \left\{ \left( {{x(t)},{u(t)}} \right) \right\}_{t} \right)}} + {J_{r}(\rho)}}{{{x_{1}\left( {t + 1} \right)} - {A_{1}{x_{1}(t)}}} = {B_{1}{u_{1}(t)}}}{{{{x_{t1}^{(i)}\left( {t + 1} \right)} - {A_{t1}^{(i)}{x_{t1}^{(i)}(t)}}} = 0},\ {{\forall i} = 1},{\ldots\mspace{14mu} N_{T}}}{{{H_{x}{x_{1}(t)}} + {H_{v}{u_{1}(t)}} + {\sum\limits_{i = 1}^{N_{T}}{H_{t1}^{(i)}{x_{t1}^{i}(t)}}}} \leq K}{{\rho^{j} \leq {{\sum\limits_{t = 0}^{N}{H_{b}^{j}{{\mathcal{z}}(t)}}} + {H_{r}^{j}{x(t)}}}}\ ,\ {{\mathcal{j}} \in \mathcal{J}_{h} \subseteq \left\{ {1,\ldots\mspace{14mu},\ n_{\phi}} \right\}}}{{\rho \leq \rho^{\mathcal{j}}},\ {{\mathcal{j}} \in \mathcal{I}_{h}}}{\rho \geq R \geq ɛ > 0}{{t = 0},\ldots\mspace{14mu},N}{{{\mathcal{z}}(t)} \in \left\{ {0,1} \right\}^{n_{\mathcal{z}}}}} & (29)\end{matrix}$

where N is the horizon of decision in DMS, x contains the states of thevehicle and the traffic, u₁ is the vehicle input according to the firstmodel, J_(p) is the performance cost, such as the linear-quadratic cost

$\begin{matrix}{J_{p} = {{\sum\limits_{t = 0}^{N}{{x(t)}^{\prime}Q{x(t)}}} + {{u_{1}(t)}^{\prime}\Theta\;{u_{1}(t)}}}} & (30)\end{matrix}$

where Q, Θ are positive semidefinite matrix weights, J_(r) is therobustness cost, such as

J_(r)=ρ′Pρ  (31)

where P is a positive definite matrix weight and R is the requestedpositive robustness score for the satisfaction of the STLspecifications. It is noted that (29) maintains a block sparsitystructure of the constraints except for the constraints due to STLformulation of the route and goal specifications in (15).

By considering the compressed form (28) for the model of vehicle andtraffic, and applying a similar construction we obtain the mixed integerprogramming problem

$\begin{matrix}{\mspace{79mu}{{{\min\limits_{{\{{{u_{1}{(t)}},{{\mathcal{z}}{(t)}}}\}}_{t},\rho,{\{\rho^{j}\}}_{j}}\ {J_{p}\left( \left\{ {u(t)} \right\}_{t} \right)}} + {J_{r}(\rho)}}\mspace{79mu}{{\underset{t = 0}{\sum\limits^{N}}{H_{u}^{c}{u_{1}(t)}}} \leq {K + {H_{x}^{c}{x_{1}(0)}} + {\sum\limits_{i = 1}^{N_{T}}{{H_{t\; 1}^{t}}_{\;}^{c}{x_{t\; 1}^{i}(0)}}}}}{{{{F_{x}{x(0)}} + {F_{0}\rho} + {\sum\limits_{{\mathcal{j}} \in \mathcal{J}_{h}}{F_{\mathcal{j}}\rho^{\mathcal{j}}}} + {\sum\limits_{t = 0}^{N}{F_{b}{{\mathcal{z}}(t)}}} + {F_{u}{u_{1}(t)}}} \leq 0},\ {{\mathcal{j}} \in \mathcal{J}_{h} \subseteq \left\{ {1,\ldots\mspace{14mu},\ n_{\phi}} \right\}}}\mspace{79mu}{{t = 0},\ldots\mspace{14mu},N}\mspace{79mu}{{{\mathcal{z}}(t)} \in \left\{ {0,1} \right\}^{n_{\mathcal{z}}}}}} & (32)\end{matrix}$

in which the number of variables is reduced but the block sparsitystructure of the constraints is completely lost.

Decision Making System

FIG. 7 describes a block diagram of the DMS according to someembodiments. The rules and goals described as natural language, i.e.,rule book and everyday language, are transformed into STL formulae usingthe language described by Equations (1), (2) and stored in a database701, stored in the memory 202, for instance in the third section 213.The Rule & Goal Selection module 702 selects from the database 701 therules and goals that apply to the current situation according to theinformation for the current and upcoming road segments, as provided 703by the Routing Module 301. The STL formulae for the current rules andgoals are converted into mixed integer constraints (15 a) according to(12), (13), (14), and they are assembled with constraints obtained fromthe motion models of vehicles and traffic 705, resulting in thepartially block structured constraints (29). In different embodiments,such may be compressed in block 704 resulting into the dense form (28).

Some embodiments are based on recognition that for the MIP solver it ismore efficient to solve problems in fully structured form, so that insome embodiments of the present invention block 704 performs atransformation to the constraints to in a full block structured form, asdetailed below.

From vehicle and traffic models 705 the model error sets for ego vehicleand traffic, W_(t) and W in (22), (26), respectively, are computedpossibly using current vehicle information from sensors and estimators,307, and provided to the block constructing a consistency constraint.The Consistency Constraint block 706 computes a robustness score

, to be enforced as a constraint (15 b), for instance in (29), that byeffectively tightens the mixed integer constraints enforcing the STLformulae to ensure that the intermediate goals computed by DMS accordingto the first model of the motion of the vehicle, allows the MPS tocompute a trajectory according to the second model of motion of thevehicle that still achieves the goal and satisfies the traffic rules.Also, from the data 703 from the Routing Module 301, the parameters ofthe cost function are adjusted 707. The constraints from 704, the costfunction from 707, and the consistency constraints 706, are combined toconstruct 708 the mixed integer programming problem in partially blockstructured form (29), or fully dense form (32). Advantageously, for theMIP solver it is more efficient to solve problems in fully structuredform, and hence the mixed integer programming problem may be constructedas in a full block structured form, as detailed below. The MIP problemis then processed by a mixed integer solver algorithm 709, whichcomputes its solution from which the information on the nextintermediate goals is extracted 710 to be provided to the MPS in themotion planning submodule 304 of the planning and control module 303. Insome embodiments of the present invention the next intermediate goalscomputed from the solution of the MIP problem are provided to the MPC aswaypoints for the trajectory, i.e., points that the trajectory need togo through.

FIG. 8 shows a flowchart of the computations performed by the DMS in asequential form according to some embodiments. These embodiments arebased on recognition that synthesizing a software program enforcingtraffic rules expressed in natural language, i.e., everyday language, iserror prone and time consuming, while it is more effective to convertthe traffic rules expressed in natural language into formulae of aformal language, and then to synthesize the software program from suchformulae. Thus, the traffic rules and goals specifications areconstructed 800 as STL formulae from natural language descriptions, suchas in driving rules books, and stored in database 700. In variousimplementations, the traffic rules can vary in different roads, not justquantitatively, i.e., how much is the maximum velocity, but also inapplicability, e.g., are there any turn restrictions, is passingallowed, etc. Thus, among the many rules in the database, the DMSselects 801 the ones that apply to the current driving conditions basedon the routing information from the routing module 301 and on the mapstored in the memory, such as the number of lanes, turn restrictions ineach lane, passing allowed, status of traffic, etc.

It is a realization of some embodiments that due to the enforced ruleschanging a controller code cannot be synthesized as a single controllerbeforehand but is adjusted continuously by adding and removing rules.Thus, some embodiments implement the DMS as an optimization problemwhere the STL formulae describing traffic rules goals are constructed802 as constraints, and the constraints are added and removed from theoptimization problem, according to the added and removed traffic rulesand goals 802. The first model of the vehicle motion and of the trafficmotion for predicting vehicle and traffic behaviors, respectively, arealso added 803 as constraints. Then, the DMS decides based on solverparameters and problem dimensions if 804 to compress the constraints toa fully dense form, that results in transforming the constraints from(27) to (28). In this case, the problem dimensions are reduced whichallows for faster solution in certain cases, especially if the originalproblem is of small dimensions. However, some MIP solver algorithms maybe more efficiently applied to problem with block structured form,resulting in reduction of memory and computing time, which allows theapproach to be applied in real-time operations. Thus, if 804 the problemis not compressed, the DMS decides based on solver parameters andproblem dimensions if 805 to expand the constraints to a fully blockstructured form.

Note that the dense and block-structured mixed-integer optimizationproblem formulation of the DMS are fully equivalent. However, someembodiments of the invention are based on the realization that theblock-structured MIP formulation can be computationally more efficientthan the fully dense MIP formulation for one or multiple of the MIPsolution 811 steps, including any pre-processing steps, the discretesearch process and the solution of convex relaxations. Examples ofpre-processing steps are domain propagation to tighten constraints onindividual discrete and/or continuous variables as well as dual fixingsand substitutions. An example of a discrete search process formixed-integer programming is a branch-and-bound optimization algorithm,which is based on successively tightening the bounds on one or multiplediscrete optimization variables and it requires the solution of convexrelaxations to construct local lower bounds to the MIP solution. Anexample of a convex relaxation of a mixed-integer quadratic program(MIQP) is based on replacing each of the discrete optimization variablesby continuous optimization variables that are each constrained to bebetween its smallest and largest discrete possible value. In addition,some embodiments of the invention are based on the realization that theblock-structured MIP formulation can be more efficient in terms ofmemory requirements than the fully dense MIP formulation in order tostore the MIP problem data, the intermediate variables in the MIPoptimization algorithm and the MIP solution vectors.

Some embodiments of the invention use an implementation of the DMS thatis based on a block-structured formulation of the MIP, in which both thelinear-quadratic cost function and the linear equality and inequalityconstraints exhibit a block-structured sparsity. More specifically, eachterm in the objective function and each inequality constraint involvesoptimization variables from the same sampling time instant as in (27).Only equality constraints, e.g., to impose a vehicle motion model suchas (17) on the state variables, can involve one or multiple optimizationvariables at two consecutive sampling time instants. Some embodiments ofthe invention are based on the realization that a lifting procedure canbe used to expand one or multiple of the equality or inequalityconstraints that involve discrete and/or continuous optimizationvariables from multiple sampling instants. Such a lifting procedureintroduces one or multiple additional discrete and/or continuousoptimization variables and it replaces each of the equality orinequality constraints, which couples variables from multiple samplinginstants, by one or multiple alternative equality and/or inequalityconstraints that involve only optimization variables from the samesampling time instant as in (27).

Given an STL formula ϕ, a lifting procedure can define optimizationvariables u_(t) ^(ϕ) and x_(t) ^(ϕ) for each sampling time instant t anddefine the following additional equality constraint x_(t+1) ^(ϕ)=u_(t)^(ϕ) that imposes the state variable x_(t+1) ^(ϕ) at time t+1 to beequal to the control input variable u at time instant t. The DMS thenensures, by defining a set of mixed-integer linear constraints, thatu_(t) ^(ϕ=)1 holds if STL robustness score of ϕ at time t is greaterthan some predefined threshold value R, i.e., ρ(ϕ, ξ, t)>R>0. Someembodiments of the invention are based on the realization that all STLformulae can be defined in a recursive manner, resulting in equality andinequality constraints that involve only optimization variables at twoconsecutive sampling time instants. In some implementations, the liftingprocedure can use additional state variables x_(t) ^(ϕ), which aredefined to be equal to the corresponding control input variable at theprevious sampling time instant x_(t+1) ^(ϕ)=u_(t) ^(ϕ), in order toreformulate all inequality constraints in terms of state and/or controlinput variables from the same sampling time instant. The liftingprocedure results in an MIP formulation with a block-structured problemsparsity that can be exploited in a computationally efficient solutionby a structure exploiting optimization algorithm.

For each predicate π^(μ), the corresponding variable u_(t) ^(μ) can bedefined as a binary optimization variable u_(t) ^(μ) ∈{0,1} and theinequality constraint μ(x_(t))+M(1-u_(t) ^(μ))>R can be defined in whichM>0 is sufficiently large and R>0 is the robustness threshold value. Theconstraint μ(x_(t))+M(1-u_(t) ^(μ))>R implies that ρ(μ, ξ, t)>R>0 holdsif u_(t) ^(μ)=1. Similarly, if there is a negation operator before apredicate ¬μ, the corresponding variable u_(t) ^(¬μ) can be defined as abinary optimization variable u_(t) ^(¬μ)∈{0,1} and the inequalityconstraint μ(x_(t))−M(1−u_(t) ^(¬μ))≤−R can be defined. The constraintμ(x_(t))−M(1−u_(t) ^(¬μ))≤−R implies that ρ(¬μ, ξ, t)≤−R<0 holds ifu_(t) ^(¬μ=)1.

Embodiments of the invention are based on the realization that Booleanoperators couple decision variables from the same sampling time instant.For example, a logical AND operator on multiple STL formulae, i.e.,ψ=Λ_(i)ϕ_(i), can be formulated as the following inequality constraintsu_(t) ^(ψ)≤u_(t) ^(ϕ) ^(i) for all i. Similarly, a logical OR operatoron multiple STL formulae, i.e., ψ=∨_(i)ϕ_(i), can be formulated as thefollowing inequality constraint u_(t) ^(ψ)≤Σ_(i)u_(t) ^(ϕ) ^(i) .Therefore, Boolean operators automatically preserve a block-structuredMIP problem sparsity.

Embodiments of the invention are based on the realization that temporaloperators typically result in constraints that couple decision variablesfrom different sampling time instants. Instead, some embodiments of theinvention are based on a recursive definition for each of the temporaloperators and define additional optimization variables in the liftingprocedure to preserve a block-structured MIP problem sparsity. Forexample, the “eventually” temporal operator can be defined in arecursive manner as follows

ρ(⋄_([a,b]) ϕ, ξ, t)=ρ(⋄_([a-1, b-1]) ϕ, ξ, t+1), if a>0,

ρ(⋄_([a,b]) , ϕ, ξ, t)=max (ρ(ϕ, ξ, t),

ρ(⋄_([0,b-1]) ϕ, ξ, t+1)), if a=0   (33)

which couples decision variables only at two consecutive sampling timeinstants. In addition, note that ρ(⋄_([0,0])ϕ, ξ, t)=ρ(ϕ, ξ, t) holds.

Based on the recursive definition of the “eventually” temporal operatorφ=⋄_([a,b])ϕ and by defining additional auxiliary decision variables,the lifting procedure can implement the DMS based on constraints thatinvolve only state and/or control input variables from the same samplingtime instant:

x _(t+1) ^(φ) =u _(i+1) ^({tilde over (φ)}), {tilde over(φ)}=⋄_([a-1, b-1])ϕ, if a>0,

x _(t+1) ^(φ) =x _(i+1) ^(ϕ) ∨u _(i+1) ^({tilde over (φ)}), {tilde over(φ)}=⋄_([0,b-1])ϕ, if a=0,

u_(t) ^(φ)=u_(i) ^(ϕ), if a=b=0,   (34)

where the additional equality constraints x_(t+1) ^(ψ)=u_(t) ^(ψ) andx_(t+1) ^(ϕ)=u_(t) ^(ϕ) have been used in order to avoid couplingbetween control input variables at two consecutive sampling timeinstants. Instead, the lifting procedure restricts the coupling betweendecision variables from consecutive time instants to be of a form wherestate variables at a particular time instant are defined by acombination of one or multiple state and/or control input variables atthe previous sampling time instant.

A similar approach can be used in the lifting procedure to formulate the“always” temporal operator ϕ=□_([a,b])ϕ as)

x _(t+1) ^(φ) =u _(t+1) ^({tilde over (φ)}), {tilde over(φ)}=□_([a-1, b-1])ϕ, if a>0,

x _(t+1) ¹⁰⁰ =x _(t+1) ^(ϕ) Λu _(t+1) ^({tilde over (φ)}), {tilde over(φ)}=□_([0,b-1])ϕ, if a=0,

u_(t) ^(φ)=u_(t) ^(ϕ), if a=b=0.   (35)

as well as the “until” temporal operator φ=ϕ₁u_([a,b])ϕ₂ as

x _(t+1) ^(φ) =x _(t+1) ^(ϕ) ¹ Λu _(t+1) ^({tilde over (φ)}), {tildeover (φ)}=ϕ₁

_([a-1, b-1])ϕ₂, if a>0,

x _(t+1) ^(φ) =x _(t+1) ^(ϕ) ² ∨(x _(t+1) ^(ϕ) ¹ Λu _(t+1)^({tilde over (φ)})), {tilde over (φ)}=ϕ₁

_([0,b-1])ϕ₂, is a=0,

i _(t) ^(φ)=i_(t) ^(ϕ) ² , if a=b=0.   (36)

while preserving the block-structured sparsity in the MIP problemformulation.

The DMS then determines 808 the required margin

in the robustness score and constructs the consistency constraint (15b). In some embodiments, the DMS and MPS use different models forvehicle motion because they need different prediction horizon, and hencedifferent precisions. Specifically, the DMS uses a first model of thevehicle motion (16), which is less precise because it needs to bepredicted for longer time while maintaining the computation time to besmall to be executed in real-time. Instead, the MPS uses a second modelof the vehicle motion (18), which is more precise because it ispredicted for shorter time, so that the computation cost will still besmall. However, if the DMS goals produced with the first model areexecuted in MPS according to a second model, the specifications that aresatisfied by DMS can be violated in MPS.

FIG. 9 illustrates the effect of computing a sequence of intermediategoals based on a first model of the vehicle and then executing the goalsin a second model of the vehicle according to some embodiments. Forinstance, in FIG. 9 the vehicle 901 is in a first lane 900 and has tomove to a second lane 903 to avoid a traffic vehicle 902 and stop at thestopline 905. The DMS computes a set of intermediate goals as waypointsbased on the trajectory 904 computed according the first model of thevehicle, such that the trajectory according to the first model of thevehicle motion connecting such waypoints is inside the area 910 wherethe STL specifications of traffic rules are satisfied. However, when theMPS executes the waypoints according to the second model of motion ofthe vehicle, the resulting trajectory 906 leaves the correct area 910,and in practice causes a collision 907 with the traffic vehicle andmisses the stop area by stopping after 908 the stopline. That occursbecause the first and the second model of vehicle motion are differentand hence a trajectory that can be executed according to the first modelmay not be executed according to the second model.

To address this inconsistency, some embodiments rather than trying tosatisfy the nominal STL formulae on the first model accounting for anypossible error difference between the first and second model, enforcewith respect to the first model the STL formulae tightened by arobustness margin. Thus, in some embodiments, the DMS determines therobustness margin

for enforcing the STL formulae to ensure that if a motion plan computedbased on the first model of the motion of the vehicle satisfies the STLformulae according to the margin

then a motion plan can be computed according to the second model ofmotion of the vehicle that still satisfies the STL formulae without suchmargin

. In some embodiments, the robustness margin

is computed based on the error set W in (22) and W_(t) in (26),

$\begin{matrix}{\mspace{79mu}{{R = {\min\limits_{R,\rho_{i}}R}}{\left. {{s.t.\ {\rho_{i}(x)}} \geq R}\Rightarrow{{\rho_{i}\left( {x + {w} + {w_{t}}} \right)} \geq 0} \right.,\ {\forall{w \in W}},\ {w_{t} \in W_{t}},{\forall{x \in X_{\rho}}},\ {\forall{i \in \mathcal{I}_{h}}}}}} & (37)\end{matrix}$

where

,

are matrices applying the error to the appropriate components of thestate vector x and all values of x in the set X_(ρ) are considered. Insome embodiments, the predicates in the STL formulae are defined bypolytopic constraints H^(i)x≤K^(i), and the robustness margin iscomputed by determining the maximum increase in the constraints causedby elements in the disturbance set W,

${{\overset{\_}{w}}_{\mathcal{j}}^{i} = {\underset{w \in W}{\arg\;\max}\;\left\lbrack {H^{i}w} \right\rbrack}_{\mathcal{j}}},{\rho_{i} = {\max\limits_{\mathcal{j}}\;{\overset{\_}{w}}_{\mathcal{j}}^{i}}},$

and then repeating the same for the traffic using the set W_(t), andcomputing

from the relations in (3). In some embodiments of the present inventionthe robustness margin is enforced by including the robustness scoreconstraint

ρ(x)≥R

and imposing that each mixed-integer logical constraints is satisfiedwith margin ρ_(i) computed from ρ and the robustness score for thecorresponding formula according to (11).

FIG. 10 shows a schematic of an effect of robustness margin whencomputing a sequence of goals based on a first model of motion of thevehicle and then executing the goals in a second first model of motionof the vehicle according to some embodiments. The effects of therobustness margin are exemplified in FIG. 10 for the same scenario asFIG. 9, where 1010 is the region where the STL formulae are satisfiedwith robustness margin, so that the DMS trajectory 1001 computedaccording to the first model is inside the region 1010, and theresulting MPS trajectory 1002 computed according to albeit not in theregion 1010 due to the difference between the first and second model, isstill inside region 910 where the formulae are satisfied.

In some implementations, the DMS then constructs 809 the cost function

J({(x(t),u(t))}_(t), ρ))=J _(p)({(x(t),u(t))}_(t))+J _(r)(ρ)=aJ_(p)({(x(t), u(t))}_(t))+(1−a) J _(r)(ρ)   (38)

which includes two terms, a performance term and a robustness term. Theperformance term J_(p) is used to enforce the desired behavior of thevehicle such as driving near the center of the lane, maintaining a speedclose to a defined target, and includes states and inputs of the firstmodel of the vehicle. In some embodiments of the present invention J_(p)is defined by a quadratic cost of states and inputs as in (30), possiblywith respect to reference values for states and inputs, r_(x), r_(u)

$\begin{matrix}{{\overset{¯}{J}}_{p} = {{\sum\limits_{t = 0}^{N}{\left( {{r_{x}(t)} - {x(t)}} \right)^{\prime}{Q\left( {{r_{x}(t)} - {x(t)}} \right)}}} + {\left( {{r_{u}(t)} - {u_{1}(t)}} \right)^{\prime}{\Theta\left( {{r_{u}(t)} - {u_{1}(t)}} \right)}}}} & (39)\end{matrix}$

The performance term J_(r) is used to increase the robustness of thesolution, and it can be formulated as a quadratic function in (31) withrespect to the robustness score ρ.

The cost function (38) contains a parameter a which determines thebalancing of the robustness objective and the performance objective. TheDMS adjusts a to the current driving condition by increasing a whenhigher performance is sought, and decreasing a when higher robustness issought, with the case of a=1 and a=0 being the limits when onlyperformance or only robustness are sought, respectively.

Then the DMS constructs 810 the MIP problem from the current state ofthe vehicle and traffic obtained from sensors and estimators, from thevehicle and STL formulae constraints, from the robustness constraint,and from the cost function,

$\begin{matrix}{{{\min\limits_{Z}{Z^{T}HZ}} + {C^{T}Z}}{{{s.t.G_{i}}Z} \leq K_{i}}{{G_{e}Z} = K_{e}}{{F_{b}Z} \in \left\{ {0,1} \right\}}} & (40)\end{matrix}$

where Z collects all the decision variables for the MIP problem, F_(b)defines what variables are Boolean, and matrices H, G_(i), G_(e), may bedense if the MIP problem if the check 804 was satisfied, partially blocksparse, if the checks 804 and 805 were not satisfied, or fully sparse ifthe check 804 was not satisfied, and the check 805 was satisfied. Theoptimal solution of MIP problem (40) is denoted by Z*.

The MIP problem is solved 811 by a MIP solver algorithm running in theprocessor 201. In some embodiments, the MIP solver is capable ofexploiting the structure of the constraints, for instance when theconstraints are transformed 807 in expanded form.

FIG. 11A shows a block diagram and FIG. 11B shows pseudo code of anexemplar branch-and-bound optimization algorithm to solve MIP accordingto some embodiments. The branch-and-bound method initializes thebranching search tree information for the mixed-integer quadraticprogram (MIQP) at the current control time step 1110, based on the MIQPdata 1145 that include MIQP matrices and MIQP vectors forming thestructure of the MIP. The initialization can additionally use thebranching search tree information and MIQP solution information from theprevious control time step 1109 in order to generate a warm startedinitialization for the current control time step 1110. The main goal ofthe optimization algorithm is to construct lower and upper bounds on theobjective value of the mixed-integer control solution. If the gapbetween the lower and upper bound value is smaller than a particulartolerance value 1111, then the mixed-integer optimal control solution isfound 1155.

As long as the gap between the lower and upper bound value is largerthan a particular tolerance value 1111, and a maximum execution time isnot yet reached by the optimization algorithm, then the branch-and-boundmethod continues to search iteratively for the mixed-integer optimalcontrol solution 1155. Each iteration of the branch-and-bound methodstarts by selecting the next node in the tree, corresponding to the nextregion or partition of the integer variable search space, with possiblevariable fixings based on pre-solve branching techniques 1115. After thenode selection, the corresponding integer-relaxed MPC problem is solved,with possible variable fixings based on post-solve branching techniques1120.

If the integer-relaxed MPC problem has a feasible solution, then theresulting relaxed control solution provides a lower bound on theobjective value for that particular region or partition of the integervariable search space. In case that this lower bound is larger than thecurrently known upper bound for the objective value of the optimalmixed-integer control solution 1121, then the selected node is pruned orremoved from the branching tree 1140. If the objective is lower than thecurrently known upper bound 1121, and the relaxed control solution isinteger feasible 1125, then the currently known upper bound andcorresponding mixed-integer control solution guess needs to be updated1130.

If the integer-relaxed MPC problem has a feasible solution and theobjective is lower than the currently known upper bound 1121, but therelaxed control solution is not yet integer feasible, then the globallower bound for the objective can be updated 1135 to be the minimum ofthe objective values for the existing nodes in the branching tree andthe selected node is pruned from the tree 1140. In addition, startingfrom the current node, a discrete variable with a fractional value isselected for branching according to a particular branching strategy1145, in order to append the resulting subproblems, corresponding toregions or partitions of the discrete search space, as children of thatnode in the branching tree 1150.

An important step in the branch-and-bound method is how to create thepartitions, i.e., which node to select 1115 and which discrete variableto select for branching 1145. Some embodiments of the invention arebased on branching one of the binary control variables with fractionalvalues in the integer-relaxed MPC solution. For example, if a particularbinary control variable u_(i,k) ∈{0,1} has a fractional value as part ofthe integer-relaxed MPC solution, then some embodiments create twopartitions of the mixed-integer program by adding, respectively, theequality constraint u_(i,k)=0 to one subproblem and the equalityconstraint u_(i,k)=1 to the other subproblem. Some embodiments of theinvention are based on a reliability branching strategy for variableselection, which aims to predict the future branching behavior based oninformation from previous branching decisions.

Some embodiments of the invention are based on a branch-and-bound methodthat uses a depth-first node selection strategy, which can beimplemented using a last-in-first-out (LIFO) buffer. The next node to besolved is selected as one of the children of the current node and thisprocess is repeated until a node is pruned, i.e., the node is eitherinfeasible, optimal or dominated by the currently known upper boundvalue, which is followed by a backtracking procedure. Instead, someembodiments of the invention are based on a branch-and-bound method thatuses a best-first strategy that selects the node with the currentlylowest local lower bound. Some embodiments of the invention employ acombination of the depth-first and best-first node selection approach,in which the depth-first node selection strategy is used until aninteger-feasible control solution is found, followed by using thebest-first node selection strategy in the subsequent iterations of thebranch-and-bound based optimization algorithm. The latter implementationis motivated by aiming to find an integer-feasible control solutionearly at the start of the branch-and-bound procedure (depth-first) toallow for early pruning, followed by a more greedy search for betterfeasible solutions (best-first).

The branch-and-bound method continues iterating until either one ormultiple of termination conditions are satisfied. The terminationconditions include the maximum execution time for the processor isreached, all the nodes in the branching search tree have been pruned,such that no new node can be selected for solving convex relaxations orbranching, and the optimality gap between the global lower and upperbound value for the objective of the mixed-integer control solution issmaller than a tolerance value.

The intermediate goals for the MPS are then extracted 812 from the MIPsolution Z* possibly as waypoints. For instance, from the sequence ofvehicle states (x*₁(t), x*₁(t+1), . . . x*₁(t+N)) according to the firstmodel of the vehicle computed according to the MIP solution, the DMSextract the time sequence within the future horizon of planning of theMPS, N_(MPS), and (x*₁(t), x*₁(t+1), . . . x*₁(t+N_(MPS))) provides 813that to the MPS, possibly with additional information about the errorset of vehicle and traffic and the robustness margin used in thecomputation, W, W_(t), R .

Some embodiments consider that in a dynamic environment, such as roadwith autonomous and non-autonomous vehicles, changing weatherconditions, etc., the predictions of the behavior of the traffic and ofthe vehicle may not be exact. Thus, it is advantageous to continuouslyevaluates the admissibility of previously computed intermediate goals,based on updated information obtained from sensors and estimators. Ifthe goals are no longer admissible, anomalies have occurred, andappropriate corrective actions are needed. It is recognized thatmonitoring is computationally more efficient than recomputing. Hence, insome embodiments, the monitoring occurs more frequently than thecontrolling to be able to catch anomalies and react rapidly, and thusthe amount of computation for the monitoring is smaller than the one forthe controlling.

Thus, some embodiments use the Monitoring and Reaction System (MRS) inthe monitoring and reactive module 320 to evaluate whether a previouslycomputed sequence of intermediate goals and waypoints is still validcording to the updated information received from sensors and estimators307.

FIG. 12 shows a flowchart of the operation of the monitoring MRSaccording to some embodiments. First, the MRS checks 1210 if the DMS hasprepared a new sequence of intermediate goals or waypoints, and if soreceives 1201 such sequence. The MRS updates 1202 the sequence bydiscarding all elements that are already in the past and substituting tothem the values received from sensors and estimators 307 at thecorresponding time instants. When the MRS receives 1203 new data fromsensors and estimators 307, it checks 1204 if the sequence ofintermediate goals and waypoints is still valid by evaluating if theupdated sequence of intermediate goals and waypoints still satisfies theinequalities of the MIP problem (40) computed from the same vehicle andSTL formulae constraints, robustness constraint, and cost function usedto compute the sequence of goals in the past when such sequence wasgenerated, but using now the most recent information on vehicle andtraffic obtained from sensors and estimators 307.

If the inequalities of (40) are not satisfied an anomaly is detectedotherwise the monitor continues at the next iteration. If an anomaly isdetected the MRS evaluates 1205 the criticality by determining if theanomaly is a vehicle safety risk, a major traffic violation or a minortraffic violation, and when such an anomaly occurs, whether in theimmediate future, e.g., within the next two cycles of updates ofdecision updates by the DMS, or in the far future, e.g., after two ofsuch DMS update cycles. It is recognized that since in monitoring theonly action is to evaluate whether the constraints of the MIP problem(40) are satisfied for the sequence of intermediate goals and waypointsupdated with the most current sensors or estimators information, ratherthan actually computing a sequence of intermediate goals and waypointsthat satisfies the constraints and minimizes the cost, the MRS performsmuch fewer computations and can hence execute at much higher rate thanthe DMS as necessary for frequent vehicle monitoring.

Then, the MRS identifies the corrective actions. In someimplementations, the corrective actions can vary based on the type ofanomaly. For example, if the anomaly is a minor traffic violation, suchas a small crossing of the sideline, or a small overspeeding, an urgentadjustment request signal is generated. If the anomaly is a majortraffic violation, such as not stopping at an intersection, or crossinginto the opposite lane, an error correction request signal is generated.If the anomaly is a vehicle safety risk, such as a predicted collisionwith traffic or pedestrians or a full out of road excursion, anemergency request signal is generated. The signals are defined of typewarning, if their triggers occur in the far future, or fault if theyoccur in the near future.

Finally, the MRS provides the anomaly information and the signals andtheir type to all the submodules of Planning and Control modules. Forinstance, warnings can be recorded and used to ignore previouslycomputed plans, while errors trigger immediate recomputation of part ofthe plans. Emergency requests can cause immediate emergency stoppinghandled by the actuator control 306, error requests can causere-computation of the trajectory by the MPS 304 and its tracking by thevehicle control 305, while urgent adjustments may be handled only byre-executing the decision-making module 302.

Exemplar Embodiments

One exemplar embodiment discloses a control system for controlling amotion of a vehicle to a target driving goal in routing selectedaccording to a desired destination of the vehicle. In oneimplementation, the control system is arranged on the controlledvehicle, such as an autonomous or semi-autonomous vehicle. In anotherimplementation, the control system is arranged on a road side unit (RSU)and commutatively connected to the controlled vehicle. The motion of thevehicle is controlled by determining and submitting control commands,such as velocity and/or acceleration values, to the actuators of thevehicle.

In various implementations, the target driving goal is selectedaccording to the desired destination of the vehicle. Examples of thetarget driving goal includes the desired destination as well as extendeddesired destination annotated with desired states of the vehicle at thedesired destination. For example, the desired destination can be anearby supermarket, while the extended desired destination can bestopping at a parking lot of the nearby supermarket. For example, thedesired destination can be exit from a highway performed in autonomousdriving mode, while the extended desired destination can be the end ofthe highway ramp with the maximum allowed or possible speed.Additionally or alternatively, the target driving goal can be a functionof a destination on a route to the desired destination. For example, thetarget driving goal can be an entrance into a region of streetscontrolled by dedicated RSU.

The control system includes a memory configured to store a first modeland a second model of the vehicle. The first model can include one orcombination of a first motion model of the vehicle and a first trafficmodel of motion of a traffic in proximity of the vehicle. The secondmodel can include a second motion model of the vehicle and a secondtraffic model of motion of the traffic. The motion models definedynamics of the motion of the vehicle as a function of time. Examples ofthe motion model can be found in Equation (16)-(19). The traffic modelsdefine dynamics of the traffic in proximity of the controlled vehicle.Examples of the traffic model can be found in Equation (23)-(26). Acombination of the motion and traffic models allows to control thedynamics of the controlled vehicle while predicting the possibledynamics of the traffic around the vehicle, which is necessary to ensurecorrect operation of the driving, for instance for avoiding collisionswith nearby traffic.

In various embodiments, the first model is an approximation of thesecond model configured to reduce an amount of computations required toevaluate the first model with respect to an amount of computationsrequired to evaluate the second model. Examples of such an approximationincludes reduction of an order of the motion model that defines a numberof state variables. For example, in one embodiment an order of thesecond model is higher than an order of the first model. Another exampleof such an approximation is simplification of equations definingdynamics of the vehicle and/or the traffic. For example, the firstmotion model can include linear equations approximating non-linearequations of the second model. In such a manner, the computationaccording to the first model is simplified with respect to thecomputation according to the second model.

The control system includes at least one processor coupled with storedinstructions implementing modules of the control system. The modulesinclude a decision-maker configured to determine a sequence ofintermediate goals leading to the target driving goal by optimizing themotion of the vehicle subject to the first model and tightened drivingconstraints formed by tightening driving constraints by a safety margin.Hence, the objective of the decision-maker module includes determinationof the intermediate goals leading to the target driving goal with anapproximated/coarse first model. Examples of the intermediate goalsdepend on the type of the target driving goal and can include staying inthe current lane, changing the lane, stopping at the stop sign beforemaking a left turn, etc.

Because different sequences of intermediate goals can lead to the sametarget driving goal, the decision-maker performs an optimization toselect an optimum sequence. The optimization is performed subject todriving constrains that include mixed logical inequalities of temporallogic formulae specified by traffic rules and the routing. Examples ofthe traffic rules include speed limits, rules for passing theintersection, preference for maintaining a position in a center of alane, as well as requirements not to collide with other vehicles andpedestrians. The traffic rules change based on the state of the firstmodel. For example, the traffic rules change in response to a change ofthe speed limit on a current section of the road, as well as in responseto a change in the traffic situations. Examples of routing includeindications to align in a specific lane before an intersection, to makea specific turn at the intersection, to turn in a different street, tointer in the highway, to leave the road to a parking lot, etc.

To that end, a control system of some embodiments is connected tovarious sensors of the controlled vehicle, sensors of other vehiclesforming the traffic and/or RSU, as well as databases of traffic rulesenabling the control system to select current traffic rules based onstate of the vehicle as well as the routing defining direction to thetarget driving goal.

Representing the traffic rules as driving constraints allows the controlsystem to reuse the same optimization routine for different trafficrules. For example, one embodiment just updates the driving constraintsin response to the change of the traffic rules while preserving theoptimization routine. To simplify the computation, the drivingconstraints include mixed logical inequalities of temporal logicformulae specified by traffic rules and the routing.

In addition to simplification of the optimization, some embodiments usethe driving constraints to account for a difference between the firstand the second models. To that end, the decision-maker performs theoptimization subject to the tightened driving constraints. Specifically,the mixed logical inequalities of the driving constraints define an areawhere the temporal logic formulae are satisfied. The tightened drivingconstraints shrink that area by the safety margin, which is a functionof a difference between the second model and the first model.

In such a manner, the intermediate goals determined based on the firstmodel but subject to tightened driving constraints can be used by moreaccurate second model with the original driving constraints. This allowsthe control system to include a motion planner configured to determine amotion trajectory of the vehicle tracking the sequence of intermediategoals by optimizing the motion of the vehicle subject to the secondmodel. Hence, the motion planner can track the intermediate goalsinstead of trying to run its own optimization routine to simplify thecomputation while preserving safety guarantees. To control the motion ofthe vehicle, the control system includes a controller configured togenerate and submit control commands to at least one actuator of thevehicle to follow the motion trajectory.

In some embodiments, the safety margin is selected such that for allstates of the vehicle satisfying the tightened driving constraintsaccording to the first model of the vehicle, there is a control inputthat transitions the state of the vehicle according to the second modelwithout violating the driving constraints. In such a manner, theoperations according to the first and second models are balanced witheach other.

There are number of different approaches for selecting the safetymargin. For example, in one embodiment, the decision-maker is configuredto determine a region of states of the first model representing adifference between states of the first model obtained by transitioningtransformations of states of the second model according to the firstmodel for a set of inputs of the second model, and states of the firstmodel obtained by transformation of states of the second model obtainedby transitioning states of the second model according to the secondmodel for a set of inputs of the second model; and determine the safetymargin for tightening the driving constraints such that, for any stateof the first model that satisfies the tightened driving constraints, acombination of the same state with any state in the region of statessatisfies the driving constraints. Such a state-based determination ofthe safety margin is advantageous because it can be computed exactly orapproximately for many choices of first and second models

Different implementations of the decision-maker module use differentoptimization solvers. For example, one embodiment solves a mixed integerproblem (MIP) that optimizes an MIP objective function subject to thetightened driving constraints to produce the sequence of intermediategoals according to a solution of the MIP. To that end, in thisembodiment, the decision-maker is configured to select the temporallogic formulae from a database of signal temporal logic (STL)specifications based on a current state of the vehicle, a current stateof a traffic and the next target location; transform the selectedtemporal logic formulas into the driving constraints; tighten thedriving constraints according to the safety margin; and solve a MIPsubject to the tightened driving constraints to produce the sequence ofintermediate goals according to a solution of the MIP. This embodimenttakes advantage of approximation of the first model to reduce thedecision making to solving the MIP.

Some embodiments use different techniques to simplify the MIP solver bypreserving a sparse structure of the MIP solution. For example, in someimplementations, the decision-maker is configured to lift the MIP into ahigher dimension by introducing one or combination of additionaloptimization variables and additional constraints to achieve ablock-sparsity of the MIP formulation; and solve the MIP in the higherdimension. Despite an introduction of additional variables, the sparsestructure of the MIP in the lifted domain can still providecomputational advantages.

To that end, in one implementation, the lifting is performed such thateach term in the MIP objective function and each MIP inequalityconstraint involves one or multiple optimization variables from the samesampling time instant and each MIP equality constraint only involves oneor multiple optimization variables from the same sampling time instantor one or multiple optimization variables from two consecutive samplingtime instants

Additionally or alternatively, in one implementation, the liftingintroduces additional optimization variables to replace each of theequality or inequality constraints that couple variables from multiplesampling time instants by one or multiple alternative equality andinequality constraints that involve only optimization variables from thesame sampling time instant, and the additional optimization variablesare state variables equal to the corresponding control input variable atthe previous sampling time instant. Examples of such lifting aredescribed in relation to the most common temporal operators, e.g.,including the temporal operators “eventually”, “always” and “until”,that can be used in the temporal logic formulae of the decision-maker.

Additionally, or alternatively, one embodiment modifies a cost functionoptimized by the decision-maker module to achieve a desired balancebetween vehicle performance, e.g., time to reach the final destination,and robustness, i.e., how much the obtained decisions are resistant tounexpected behavior of the environment. For example, in oneimplementation, the decision-maker optimizes a cost function including afirst term encouraging an achievement of the next target goal and asecond term encouraging an increase of the safety margin. An example ofthe term encouraging an achievement includes the distance from the nexttarget. An example of the term encouraging an increase of the safetymargin includes a coefficient defining the safety margin above theminimum. Such a modification allows to adjust relative importance of thefirst and second term based on the current traffic conditions bymodifying a non-negative weight parameter in the cost function.

In some embodiments, the modules of the control system include ananomaly detector that can take advantage of cheaper computations ofdecision maker to test whether there is a danger to the safety of thevehicle and/or whether the more computationally expensive motion plannerneeds to be re-executed. To that end, the anomaly detector is configuredto periodically receive the sequence of intermediate goals determined bythe decision maker for the tightened driving constraints; update thetightened driving constraints based on a change in the state of thefirst model defining a change in the states of the vehicle and thetraffic; test whether the sequence of intermediate goals violates theupdated tightened driving constraints; and, upon detecting theviolation, execute a corrective action. In such a manner, the vehiclecan still be controlled according to determined trajectory even whensome changes in the state of the vehicle and/or traffic took place.

For example, in one implementation, to update the tightened drivingconstraints, the anomaly detector is configured to receive updatedinformation from sensors on current and past positions of the controlledvehicle and the traffic; and determine the tightened driving constraintsfor the updated current and past positions on the vehicle and thetraffic. The current and past positions of the controlled vehicle andthe traffic can be received from various sensors operatively orcommunicatively connected with the controlled system. Such an updateallows some embodiments to test the violation of the updated drivingconstraints on the same optimization used for determining the sequenceof intermediate goals. For example, when the optimization is performedby solving a mixed integer problem (MIP), the testing whether thesequence of intermediate goals violates the updated tightened drivingconstraints results in testing linear inequalities, which iscomputationally efficient.

In different embodiments, the corrective action is selected based on thetype of anomaly. For example, the type of anomaly includes one orcombination of a vehicle safety risk, a major traffic violation, and aminor traffic violation. For example, the corrective action includes oneor combination of an immediate emergency stopping, a re-computation ofthe motion planner trajectory, and a re-execution of the decision-makingmodule. In such a manner, the controlled system can react to the anomalysituation promptly.

The above-described embodiments of the present invention can beimplemented in any of numerous ways. For example, the embodiments may beimplemented using hardware, software or a combination thereof. Whenimplemented in software, the software code can be executed on anysuitable processor or collection of processors, whether provided in asingle computer or distributed among multiple computers. Such processorsmay be implemented as integrated circuits, with one or more processorsin an integrated circuit component. Though, a processor may beimplemented using circuitry in any suitable format.

Also, the various methods or processes outlined herein may be coded assoftware that is executable on one or more processors that employ anyone of a variety of operating systems or platforms. Additionally, suchsoftware may be written using any of a number of suitable programminglanguages and/or programming or scripting tools, and also may becompiled as executable machine language code or intermediate code thatis executed on a framework or virtual machine. Typically, thefunctionality of the program modules may be combined or distributed asdesired in various embodiments.

Also, the embodiments may be embodied as a method, of which an examplehas been provided. The acts performed as part of the method may beordered in any suitable way. Accordingly, embodiments may be constructedin which acts are performed in an order different than illustrated,which may include performing some acts concurrently, even though shownas sequential acts in illustrative embodiments.

Although the invention has been described by way of examples ofpreferred embodiments, it is to be understood that various otheradaptations and modifications can be made within the spirit and scope ofthe invention. Therefore, it is the object of the appended claims tocover all such variations and modifications as come within the truespirit and scope of the invention.

Claimed is:
 1. A control system for controlling a motion of a vehicle toa target driving goal in routing selected according to a desireddestination of the vehicle, the control system comprising: a memoryconfigured to store a first model including one or combination of afirst motion model of the vehicle and a first traffic model of motion ofa traffic in proximity of the vehicle and a second model including asecond motion model of the vehicle and a second traffic model of motionof the traffic, wherein the first model is an approximation of thesecond model; and at least one processor coupled with storedinstructions implementing modules of the control system, the modulescomprising: a decision-maker configured to determine a sequence ofintermediate goals leading to the next target goal by optimizing themotion of the vehicle subject to the first model and tightened drivingconstraints formed by tightening driving constraints by a safety margin,wherein the driving constraints include mixed logical inequalities oftemporal logic formulae specified by traffic rules and the routing,wherein the mixed logical inequalities define an area where the temporallogic formulae are satisfied, wherein the tightened driving constraintsshrink the area by the safety margin, and wherein the safety margin is afunction of a difference between the second model and the first model; amotion planner configured to determine a motion trajectory of thevehicle tracking the sequence of intermediate goals by optimizing themotion of the vehicle subject to the second model; and a controllerconfigured to generate and submit control commands to at least oneactuator of the vehicle to follow the motion trajectory.
 2. The controlsystem of claim 1, wherein the safety margin is selected such that forall states of the vehicle satisfying the tightened driving constraintsaccording to the first motion model of the vehicle, there is a controlinput that transition the state of the vehicle according to the secondmotion model without violating the driving constraints.
 3. The controlsystem of claim 1, wherein the decision-maker is configured to determinea region of states of the first model representing a difference betweenstates of the first model obtained by transitioning transformations ofstates of the second model according to the first model for a set ofinputs of the first model, and states of the first model obtained bytransformation of states of the second model obtained by transitioningstates of the second model according to the second model for a set ofinputs of the second model; and determine the safety margin fortightening the driving constraints such that, for any state of the firstmodel that satisfies the tightened driving constraints, a combination ofthe same state with any state in the region of states satisfies thedriving constraints.
 4. The control system of claim 1, wherein thedecision-maker is configured to select the temporal logic formulae froma database of signal temporal logic (STL) specifications based on acurrent state of the vehicle, a current state of a traffic and the nexttarget location; transform the selected temporal logic formulas into thedriving constraints; tighten the driving constraints according to thesafety margin; and solve a mixed integer problem (MIP) subject to thetightened driving constraints to produce the sequence of intermediategoals according to a solution of the MIP.
 5. The control system of claim4, wherein the decision-maker is configured to lift the MIP into ahigher dimension by introducing one or combination of additionaloptimization variables and additional constraints to achieve ablock-sparsity of the MIP formulation; and solve the MIP in the higherdimension.
 6. The control system of claim 5, wherein the lifting isperformed such that each term in the MIP objective function and each MIPinequality constraint involves one or multiple optimization variablesfrom the same sampling time instant and each MIP equality constraintonly involves one or multiple optimization variables from the samesampling time instant or one or multiple optimization variables from twoconsecutive sampling time instants.
 7. The control system of claim 5,wherein the lifting introduces additional optimization variables toreplace each of the equality or inequality constraints that couplevariables from multiple sampling time instants by one or multiplealternative equality and inequality constraints that involve onlyoptimization variables from the same sampling time instant, and theadditional optimization variables are state variables equal to thecorresponding control input variable at the previous sampling timeinstant.
 8. The control system of claim 7, wherein the optimizationvariables include one additional input variable and one additional statevariable for each temporal logic formula at each sampling time instant;wherein the additional input variable takes value one if thecorresponding temporal logic formula is satisfied with a predeterminedrobustness score; the additional state variable is equal to theadditional input variable corresponding to the same formula at theprevious sampling time instant; and the temporal logic formulae areconstructed iteratively from the predicates by combinations based onlogical and temporal operators.
 9. The control system of claim 1,wherein the decision-maker is configured to optimize a cost functionincluding a first term encouraging an achievement of the next targetgoal and a second term encouraging an increase of the safety margin. 10.The control system of claim 9, wherein the relative importance of thefirst and second term is adjusted based on the current trafficconditions by modifying a non-negative weight parameter in the costfunction.
 11. The control system of claim 9, wherein the decision-makeris configured to optimize the cost function over a first predictionhorizon, wherein the motion planner is configured to generate the motiontrajectory iteratively over a second prediction horizon that is shorterthan the first prediction horizon.
 12. The control system of claim 1,wherein the modules of the control system include an anomaly detectorconfigured to periodically receive the sequence of intermediate goalsdetermined by the decision maker for the tightened driving constraints;update the tightened driving constraints based on a change in the stateof the first model defining a change in the states of the vehicle andthe traffic; test whether the sequence of intermediate goals violatesthe updated tightened driving constraints; and upon, detecting theviolation, execute a corrective action.
 13. The control system of claim12, wherein to update the tightened driving constraints, the anomalydetector is configured to receive updated information from sensors oncurrent and past positions of the controlled vehicle and the traffic;and determine the tightened driving constraints for the updated currentand past positions on the vehicle and the traffic.
 14. The controlsystem of claim 12, wherein the testing violation of the updated drivingconstraints is performed on the same optimization problem used fordetermining the sequence of intermediate goals, wherein the optimizationis performed by solving a mixed integer problem (MIP), such that testingwhether the sequence of intermediate goals violates the updatedtightened driving constraints results in testing linear inequalities.15. The control system of claim 12, wherein the corrective action isselected based on the type of anomaly, wherein the type of anomalyincludes one or combination of a vehicle safety risk, a major trafficviolation, and a minor traffic violation, and wherein the correctiveaction includes one or combination of an immediate emergency stopping, are-computation of the motion planner trajectory, and a re-execution ofthe decision-making module.
 16. A method for controlling a motion of avehicle to a target driving goal in routing selected according to adesired destination of the vehicle, wherein the method uses a processorcoupled to a memory storing a first model including one or combinationof a first motion model of the vehicle and a first traffic model ofmotion of a traffic in proximity of the vehicle and a second modelincluding a second motion model of the vehicle and a second trafficmodel of motion of the traffic, wherein the first model is anapproximation of the second model, wherein the processor is coupled withstored instructions implementing the method, wherein the instructions,when executed by the processor carry out steps of the method,comprising: determining a sequence of intermediate goals leading to thenext target goal by optimizing the motion of the vehicle subject to thefirst model and tightened driving constraints formed by tighteningdriving constraints by a safety margin, wherein the driving constraintsinclude mixed logical inequalities of temporal logic formulae specifiedby traffic rules and the routing, wherein the mixed logical inequalitiesdefine an area where the temporal logic formulae are satisfied, whereinthe tightened driving constraints shrink the area by the safety margin,and wherein the safety margin is a function of a difference between thesecond model and the first model; determining a motion trajectory of thevehicle tracking the sequence of intermediate goals by optimizing themotion of the vehicle subject to the second model; and generating andsubmitting control commands to at least one actuator of the vehicle tofollow the motion trajectory.
 17. A non-transitory computer readablestorage medium embodied thereon a program executable by a processor forperforming a method, the method comprising: accessing a first modelincluding one or combination of a first motion model of the vehicle anda first traffic model of motion of a traffic in proximity of the vehicleand a second model including a second motion model of the vehicle and asecond traffic model of motion of the traffic, wherein the first modelis an approximation of the second model; determining a sequence ofintermediate goals leading to the next target goal by optimizing themotion of the vehicle subject to the first model and tightened drivingconstraints formed by tightening driving constraints by a safety margin,wherein the driving constraints include mixed logical inequalities oftemporal logic formulae specified by traffic rules and the routing,wherein the mixed logical inequalities define an area where the temporallogic formulae are satisfied, wherein the tightened driving constraintsshrink the area by the safety margin, and wherein the safety margin is afunction of a difference between the second model and the first model;determining a motion trajectory of the vehicle tracking the sequence ofintermediate goals by optimizing the motion of the vehicle subject tothe second model; and generating and submitting control commands to atleast one actuator of the vehicle to follow the motion trajectory.